Arithmetic Progressions | Complete NCERT WITH BACK EXERCISE in 1 Video | Class 10th Board

[@Class10th-UDAAN]

At 55:02, There is typing mistake in the question, it is 7 ki power 3 and not 73. And thus it will not be an AP. At 3:00:49 There is a calculation mistake, d will be 7/3 and not 5/2, accordingly answer correct krlena. Really Sorry for the mistake babuas.

[@Zoya_Ansari340]

Its ohk sir... ☺

[@g_u_r_u_k_i_s_e_w_a_3247]

Sir aap hamari itni help karte ho agar aapse choti si mistake ho gayi toh kya hogya sir . Love you Babuas❤♥️

[@MeriJaanMustafa]

4:52:49 370 metres

[@MeriJaanMustafa]

Thank you so much sir

[@MeriJaanMustafa]

May Allah bless you

[@AFSHEENMULLA-sq2nw]

At 55:20, Its 73 not 7 power 3, ans is- mentioned below: [xv] 1,25,49,73 d= a2- a1 , d= a3-a2 , d= a4-a3 = 25 - 1 = 49-25 = 73-49 = 24 = 24 =24 here, a2-a1=a3-a2=a4-a3 hence it forms an AP.. Next 3 terms are, a5=a+4d , a6=a+5d ,a7=a+6d = 1+4[24] =1+5[24] = 1+6[24] =1+96 = 1+ 120 =1+ 144 = 97 = 121 = 145

[@Exclusive.sohail]

Right wahi mai dekhne aya

[@Editsbythakur]

Yes true bro ncert mein answer ha but how sir didn't noticed it

[@poonamsingh7754]

Your comment should go above so sir can see it.

[@AFSHEENMULLA-sq2nw]

ya

[@AFSHEENMULLA-sq2nw]

@@Editsbythakur hmm

[@Class10th-UDAAN]

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[@kishlayanandanand]

Hi sir please reply me

[@shivam_y192]

​@@kishlayanandanandkitna percent aay?

[@PiyushMaurya-pi7tu]

Kitna percent aya bhai 😢​@@kishlayanandanand

[@yashvishwakarmadreamers75]

2:25:33 d=5 , a= -13 , a2= -8 , a3=-3

[@seema9051]

How pls explain

[@sadanandsingh249]

Sir ham logo ke liye Puri rat jagkar lecture record kiye isliye hamara bhi farj banata hai ki ham bhi acche se padhkar sir ko proud feel karwaye 😢❤❤❤❤

[@shivam_y192]

kitna percent aay?

[@gamerstot586]

Compartment agya

[@gamerstot586]

😅

[@ShortsShtick]

​@@gamerstot586 hi FF player

[@ShortsShtick]

Hi ❤ FF player 😁

[@7EDITS247]

At 1:37:00 it should be Let the first term of the AP be a and the common difference be d. Given, 11th term = 38 a + 10d = 38 ...(1) 16th term = 73 a + 15d = 73 ...(2) Subtracting equation (1) from equation (2), we get: 5d = 35 d = 7 Substituting the value of d in equation (1), we get: a + 10(7) = 38 a + 70 = 38 a = -32 Now, to find the 31st term (a31): a31 = a + (31-1)d a31 = -32 + (30)(7) a31 = -32 + 210 a31 = 178 Therefore, the 31st term of the AP is 178.

[@kasturimulik4635]

4:07:31 Ans - Hence the sum of first 40 positive integers divisible by 6 is 4920

[@promanboi]

correct😀😃

[@nirmalghosh1391]

Indian ho tohh like karke 96 percent le gayu

[@Itz_Yuvraj_360]

😅😅

[@SmritaTiwari-nf9hp]

Main to bhartiya hun

[@awesomeearts3405]

Main toh nepali hu

[@IndarjitSingh-ej7es]

Mai Tera bhai hi

[@IV-X_facts]

​@@awesomeearts3405same syllabus hota hai?

[@Zunaisha1254]

We will miss you sir.... After 10th 😢

[@ChetanNaithani]

Fail. Na hoiyo kahi miss nhi karna padegq

[@kusumlatabothra5446]

​@@Education.shorts0012 messi is the goat

[@Education.shorts0012]

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[@sanskarnagda0077]

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[@prakharsinha1007]

uday 11th jake dekho

[@AdarshV-gy8vt]

No giving like at this comment ? Ok then fail in class 10th 2025 😁🤪 Edit - me be like-- 'ARE MERE TOH SIR SE JYADA LIKE HO GAYE HAI 🤣' ''SIR- RUK BETA ABHI BATA TA HU 🤣🤣''

[@kumarshambhu9331]

Kya board wala tumhara baap hai

[@AdarshV-gy8vt]

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[@muskaanshaheen2481]

​@@AdarshV-gy8vtshakal teri unke ghar safai karne ki nhi hogi

[@Virat-8cr]

Abhi tumharae upar Andi bandi chdha degae 😂

[@RAJKUMARI-dq9jh]

😅

[@jawadchouhan8046]

Time stamp 00:00-Introduction 02:19​ - Exercise - 5.1 55:21​ - Exercise - 5.2 02:36:39​ - Exercise - 5.3 04:52:55​ - Exercise - 5.4 (Optional) 05:48:33​ - Thank You !

[@ranjitsingh-tr1xi]

55:18 there is not any typing mistake see in book and the answer is it will be an AP and three more terms are 97,121,145 please check it 🙏🏻

[@Panther6825]

Yes you are right 😊😊😊

[@Panther6825]

Hello

[@Panther6825]

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[@Panther6825]

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[@Panther6825]

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[@inaam_aiimsdelhi]

4:53:08 lov3 u sirrr❤❤❤❤ from kashmir✨️❤️

[@romeelaali]

Aww I am from Kashmir too

[@KISHANENERGYWALLA]

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[@SS_SangitaSinha2322]

Aise kyu krte ho bhai😢😢

[@eren_yeager141.]

Yeah, like we would pass just by liking your comment, tf?

[@Nagvanshieus]

Bhok me ja

[@harshiogre]

Reported bro 😊

[@Thethunderanime]

Tu fail hoga 😂 chal dafa ho

[@kasturimulik4635]

4:08:42 Ans - Hence, the sum of first 15 multiples of 8 is 960.

[@tirthsoni7087]

3:18:31 Ans is wrong:(32) Correct ans :(34)

[@vidyahakke3777]

yessss

[@AnishKumar-sg8nr]

Yaa❤

[@shubhmishra7501]

Give attendance who starting their syllabus in 12 hours ago 😅😂

[@Dimpleprajapat-qn2ee]

KIS KIS KE 99.9% AAYENGE ATTENDENCE LGAO🙂👍edit: ATTENDENCE LGA DO JLDI SE ITNA MT SOCHO.🙂👍THIK HAI !

[@Niyati-cx3tj]

"Watching Day before exam"likhne vale har jagah milege 💀

[@Soumyyadav80312]

💀 frr

[@IamStill_in2019]

On the day of exam 🗿

[@Priyoxd.]

Watching in exam

[@prachi_2008i]

Us moment😂

[@DARK-lh3qn]

Me abhi dekh raha hu parso meri exam hai

[@sabasultana1336]

3:24:08 Answer - We know that, an = a + (n − 1) d a4 = a + (4 − 1) d a4 = a + 3d Similarly, a8 = a + 7d a6 = a + 5d a10 = a + 9d Given that, a4 + a8 = 24 a + 3d + a + 7d = 24 2a + 10d = 24 a + 5d = 12 ... (i) a6 + a10 = 44 a + 5d + a + 9d = 44 2a + 14d = 44 a + 7d = 22 ... (ii) On subtracting equation (i) from (ii), we get, 2d = 22 − 12 2d = 10 d = 5 From equation (i), we get a + 5d = 12 a + 5 (5) = 12 a + 25 = 12 a = −13 a2 = a + d = − 13 + 5 = −8 a3 = a2 + d = − 8 + 5 = −3 Therefore, the first three terms of this A.P. are −13, −8, and −3.

[@TanavGuptaCSK967]

3:00:15 sir a¹³ is 35 not 25 in Q3 2nd part . Sir please check .Thank you Sir 🫸🫷🫸🫷. You teach with very hard work day and night💛

[@shrutitiwari7033]

absolutly

[@shrutitiwari7033]

right

[@Swarnkar793]

~ But in another method the answer is absolutely correct 💯 (Sn = n/2[a+a13] 👍🏻

[@AbaanKhan-v7m]

Next topper+physics wallah ❤✨💯.

[@MrUjjwalhere]

Mai 😂

[@YatharthJiniya]

😂me

[@riasingh1698]

1:38:47 In exercise 5.2 Q7 answer is -178. beacause a will be -32

[@DeepikaKunwar-vn8sf]

Are aage or karna hai kauki A = -32 hai. or kar aa jayga 178 ok 😊

[@villager0123]

3:18:37 there is a mistake done in vi question The value of An =34 and not 32 An=a+[n-1]d =2+[5-1]8 =2+4×8 =2+32 =34 Hope this help

[@SnowAmI002]

Love you sir aisa teacher literally mainai apnai hole life time mai nahi dheka jab sai padhna suru kiya hu sir aab ham log 11 mai chale jayengai baas meroko aap sai hi maths padhna hai so all student vote for babua sir in class 11 ❤❤😘

[@btsarmyshivangi5182]

✨ Topics covered ✨ 00:00​ - Introduction 02:19​ - Exercise - 5.1 55:21​ - Exercise - 5.2 02:36:39​ - Exercise - 5.3 04:52:55​ - Exercise - 5.4 (Optional) 05:48:33​ - Thank You !

[@krithikasai]

Thanks bro

[@btsarmyshivangi5182]

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[@krithikasai]

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[@btsarmyshivangi5182]

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[@jigsboss5206]

Your insta id 😅

[@sahuvolgs]

1:38:52 answer is wrong because value of d in negative and the final answer is 178

[@aszfact44966]

Sahi bola bhai

[@BLUEBUNNY999]

Right

[@Naruto_uzumaki_482]

Not d value of a is negative

[@AfrinShaikh-y6l]

​@@Naruto_uzumaki_482padhai karle bha

[@mohdafzal4014]

Haa isliye nagative mai ans nahi nikalna chahiye ❤

[@laddugamer9817]

I see this video 1day before maths exam 😮😢😢

[@op_hemanta_op9653]

Us bro us me on the exam day 😢

[@Atharvashukla123]

​@@op_hemanta_op9653why,?..??

[@Sbrahma717]

Failerr

[@laddugamer9817]

No failer I got 77% in class 10 only study one day before exam. 😌😌😌😁😁

[@azfarkhan5856]

55:26 Question no 1 1:03:16 Question no 2 1:05:48 Question no 3 1:20:10 question no 4

[@Akash67817]

3:02:47 common different are wrong right Answer d = 7/3

[@KavitaPandey-s7i]

Kabhi harna mat bhaiyo jung chal rahi hai hamare or board ke bicme💪💪💪💪💪💪💪💪🤛🤛

[@Jazzzystarluiz]

We will be missing our babua😢❤

[@NishuPal-ll2ir]

Hi

[@Sbrahma717]

I

[@DPP20]

3:34:05 it can be solved by middle term splitting and the answer would be n=12

[@DIVYAPRATAPEDITS]

2024-25 wale bacche like kre 👽👍🏻

[@RoshanKumar-vt9tn]

Hi

[@prashanttyagi7395]

Ham nhi karanga

[@DIVYAPRATAPEDITS]

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[@prashanttyagi7395]

@@DIVYAPRATAPEDITS Ohh I thinking about you who are you ☺️

[@kanchan_1221]

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[@manawaralam7]

Finally completed the NCERT questions Hat's off to you sir, we are proud to have you

[@studywithtulika]

3:10:45 the answer will be 85/3 not -85/3

[@sakshamramteke3the233]

hats off sir , recorded this lecture from 12 am to 8 am , literally helped so much miss you 🥺🥺🥺🥺

[@sujalmishra684]

​@@shaghilzubairbhai sir ne subhah tak padhaya hai.

[@technicalaayu8714]

oh wow Sir ne neend hi tyag di😭😭😭😭😭😭😭😭😭

[@kasturimulik4635]

4:12:16 Ans Hence, The sum of odd numbers between 0 and 50 is 625

[@DebashisTripathy-tm7sb]

2024-25 bale attendance laga do jaldi 🎉🎉 if you want to scored 99 Percent in board exam 🎉🎉 like karo jaldi🎉🎉

[@soniyaravi7841]

100 launga me

[@RenuSingh-do5rb]

Ma 1ooo launga

[@LovelySisodiya-cx3mo]

Yahi toh problem h hamari wants poori nhi hoti

[@Kshitij326]

By this l find sir age 26 in 2024❤❤❤ like for good grades in 2025 board 😅😅

[@madhudubey9705]

duniya mein bahut hi km aise teacher hote Hn Jo hm jainse bacchon ke liye itna sochte h , mad respect sir aap Jaise teacher ki vajah se hi India ke bacchon ka future better ho raha h ❤.....

[@Memesoftheinternit]

3:18:37 the answer is 34 not 32

[@nehakausar8673]

4:52:51 sir answer is 370 for question no 20 of ex 5.3

[@AkarshKumar-c4f]

No. Answer is 275

[@AkarshKumar-c4f]

Corre😅 Sorry it is 370

[@feehaara9683]

4:35:24, the answer of Q.18 of ex. 5.3 is 143

[@umeshgupta2903]

ॐ जय मां सरस्वती ॐ 100 / 100 in both HALF YEARLY AND BOARDS EXAM in MATHS मेरी मां सदा मेरे साथ❤

[@divyagadher2825]

13:31 in this part can we take value of x 54 , 55 ,72 ,61 ,89.........etc. Then, by subtracting 1/4 We will get (d) ....

[@killedbylavitra]

Massive respect sir . Aapne subha ke 8 baje tak record kara lecture hamare liye . Ab hum boards me phod ke aaenge and all credits to you

[@kasturimulik4635]

4:16:54 Ans Hence, the contractor has to pay ₹27750, if the delayed the work.

[@rahulyt3260]

Date 9 Feb 2024 Board Exam - 21 Feb Hindi Doing maths

[@aadiyadav_77]

At 3:18:28 sir apne 8x5 kra =40 aaya then -6 kra to sir ne by mistake 32 likh Diya wha pr 34 aayega 😅😂this mistake take my 15 min to recheck all ❤❤

[@Kaunaaditya]

4:49:32 this was crazy ....Chori !! Apne yha UP m aise hi bolte h 😁

[@young_syl_15]

Sir at 2:31:58 the last term or the year should've been 2005 in my opinion, because Sir, a1=1995=5k, a2=1996=5.2k, a3=1997=5.4k, a4=1998=5.6k, a5=1999=5.8k, a6=2000=6k, a7=2001=6.2k, a8=2002=6.4k, a9=2003=6.6k, a10=2004=6.8k, a11=2005=7k.

[@Cinderella_celeste]

Batch 2024-25 attendance here...... 🌟🙋🏻‍♀️

[@ASHISHSINGH-iu6fx]

💫 🙋

[@Sarahkhan-c2z]

✋🏻

[@meenudwivedi2524]

Kyu tm teacher ho

[@Cinderella_celeste]

@@meenudwivedi2524 kyu ho nhi skti kya? 😏

[@NizamuddinTantray]

🙋‍♀️👑

[@mahabubalam6650]

One mistake in 55:20 in exercise 5.1 question no. 4 part 15(xv) that will be AP sir 1,,25,49,73 So there will be common difference of 24

[@opnatickverma5779]

Kon kon top 10 toppers mae ana cahata hae 🎉🎉🎉

[@mohdafzal4014]

Me

[@hurrainirfan4539]

5:14:36 The correct quadratic equation is a² - 6a + 8 = 0 ( reason: - 24 + 32 = +8 ) Therefore , the values are: a = 4 , a = 2 d = - 1/4 , d = 1/4 S16 = 34 , S16 = 62

[@actiongaming5229]

Who wants babua to teach in 11th class

[@Asitasit56]

🙋🙋

[@shivam_y192]

Kitna percent aay?

[@mohdafzal4014]

3:38:54 🎉

[@MenkaKumariverma]

5:12:11 pata tha ki Galt hua hai but koi nhi hm nhi likhe the 😊❤

[@Lakshya_Garhekar_15]

3:34:54 The answer is 12 terms

[@jyothihs2629]

🎉

[@Saini_Yash_editz]

4:17:22 😊❤ bilkul ji ❤.. I'm agree sir.. thanks for this💗

[@AnupaShaw-t1p]

55:20 sir aapne galti kardi woh AP hain

[@JyotiChaurasiya-xt4cx]

I'm the one who's watching this video one day before board exam on 2X 😅🤣💜

[@JyotiChaurasiya-xt4cx]

@@bp_sh3ll thanks for company sis💜🥹

[@ChetanNaithani]

❤

[@VipinYadav-iu9ob]

2:25:39 A=12. Hw1 D=5 From which using formula the ap is 12,17,22 May be this to helpfull for you With best regards Harshit yadav Hw2 2093 2:52:52

[@snipershoot5957]

Bhai mera A=-13 aarha hai shi hai? Or d 5

[@Amrita_Singh001]

Guys kis kis ka focus bas maths par hai or maths ke alawa kuch bhi padhne ka man nhi kar rha hai😅😅😅

[@Maahiee]

Mera 😭

[@Amrita_Singh001]

@@Maahiee ham but abhi to sab leke chlna padega ham kar nhi rahe wo baat alag hai

[@akshatmsharma40]

arey same broo😭😭insta ya kisi pr baat kre ek dusre se puchte rhenge ki kiska kitna huaa ??

[@dhruvv077]

Ab to padhle bhai 💀💀💀💀💀​@@akshatmsharma40

[@Maahiee]

@@dhruvv077 😭😭

[@yasirabbas6416]

Sir mad respect of you lagatr 6 hour pdhana har kisi ke baski bat nhi 😢 aap bhaut machanae wale ho life mai

[@Angelyadav065]

3:18:30. a5=34

[@SyedSadiqMosavi]

1:39:47 answers is 168✅ 178❌ Those who agree please likes❤

[@sakshi-gl5pj]

Had off to the hardwork of you sir we are luckiest student having you as our teacher I wish one day me too become hardworking like you lastly thankyou from the bottom of our heart for providing us your support 😊😊

[@_canveses_by_bitupan_]

5:15:46 🙌🌼❤ sir ka liya hat's off to banta hai yaarr 🎉

[@Cristiano-t9o2o]

3:11:11 answer is not in -ve

[@Priyoxd.]

Exactly it's not in -5

[@Cristiano-t9o2o]

@@Priyoxd. Yeah

[@Priyoxd.]

@@Cristiano-t9o2o is -5 correct?

[@Cristiano-t9o2o]

@@Priyoxd. No

[@VanshikaMittal-i2w]

At 3:57:47 , bss yaha tak dekh ke pura ques. khud se solve krr liya ...........thank you sir jii ❤❤❤❤🥳🥳

[@0_PatHAAN]

Thanks pw for providing these one shots for revision. Its really help me alot in my revision ❤

[@CricaShow]

AT 2:08:09 Please Listen 👂 😂😂😂😂

[@Prateeksha.956]

2024_2025 me boards dene vale attendance lagaye dekhe kitne bachhey is bar board denge...

[@alise7430]

Yes ma'am

[@Ravimourya4321]

1:38:45 answer will be 178 because the value of a is -32

[@ShiyuSharma-j6o]

Babua is our emotion💓✨

[@feehaara9683]

4:52:51 the ans of Q.20 is 280m

[@angelina243]

No bro, it's 370 m

[@Triggered_423]

1:38:50 negative sign ko bhul gye Babua

[@Cakesbyyashika]

1:38:50 I was also watching for it😅

[@Triggered_423]

Nostalgia 👏now in 11th learning same thing sequence series advance version of ap👏.​@@Cakesbyyashika

[@IamStill_in2019]

​@@Triggered_423 After 1 year I would also write such things.. 😮‍💨

[@IamStill_in2019]

​@@Triggered_423time goes fast fr... 😓

[@Studywithclass10student]

Kya koi ise pura ek sath dekh paya kya 😮😮😮😢😢😢😢😊😊❤❤ Who noticed ( Mude pata chala ki )😂 so cute 😊😊😊😊 Thank you sir 🎉🎉❤❤ For your efforts ❤ Hats off sir 🤗🤗🤗🤗

[@squarkingyt1659]

Thank you sir you are help me in school punishment 😢😢 thank you so much❤❤❤😊😊😊😊😊😊😊 2:03:07

[@x4.jyoti_]

He Bhagwan mai sohyega kab!!! Phir 4:00 am se live bhi krni hai....💀😩

[@RajSingh-tq6xv]

Kaisa gaya maths 🤣

[@RajSingh-tq6xv]

❓❓

[@RajSingh-tq6xv]

Hello

[@abhaymaurya5182]

Hi

[@ArtandcraftwithKimi]

4:20:39 this question is important for SEBA students

[@Aryan00345]

Give attendence who starting thier syllabus in January😅😅

[@parisharma689]

Me 😂

[@neetaspirant3641]

Bhi mai February mai start kaunga

[@SHREYANSHVARSHNEY]

Padhle

[@kavitarai9433]

🤚🏻😂

[@Maahiee]

Mai 😢

[@untimetgamer6695]

3:00:15 per upane 75 ki jagha 25 kr diya hai

[@AbhishekKumar-000]

1:39:00 sir a=-32 hoga

[@pw_motivation_0]

Hats off hain yaar sir aapko itna bhi koi aakhir kaise padha sakta hain ❤

[@HELLO_2026K]

Sir plz get some sleep hmare lie aap puri raat aab bs record hee krte rhe❤❤

[@Shivanshurpratapsingh]

In 5.3 exercise Question 3(2) mein d = 5\2 hoga na ki 3/2 Wrong 😅 3:00:12

[@MalaShrivastav-jo3wr]

Babua also said sorry for this maybe some calculations problems..... So go and see pinned comments💬

[@Shivanshurpratapsingh]

@@MalaShrivastav-jo3wr thanks bro

[@irshadahmadirshadahmad5258]

Jo question dekhne aya tha ..vo homework de diya 🥲🥲

[@19narenparmar93]

3:00:10 SIR YOU HAD MADE A MISTAKE HERE COMMON DIFFERENCE IS 7/3 ✅ NOT 3/2 ❌

[@adhyangarg4722]

Kon abhi dekh raha hau 😅😅😅

[@memeloverspoint706]

Mai to ab dekhna shuru kiye 💀

[@KanakSharma-pm6ez]

Mein

[@AnupJaitan]

Ham 100 persent Lena chata ha

[@Purvasoni1087]

Aap

[@hsvlogs4781]

Mai bhi abhi dekh ra hu sir ji ❤❤

[@Cute_Riya1001]

2:27:26 sir ka brithday year pta chal gya😁

[@user_Piyush_636]

Previous year question paper ka MCQ and ASSERTION & REASON aur CASE BASED QUESTION ka practice kara Dejeya •

[@rashmisinghsingh1688]

Bro can you tell that how many percent you got ?

[@Luckytripathi..]

4:34:29 villager sound like minecraft😮

[@ilishasrivastava6166]

3:18:32 sir (a)n or a(5) should be 34 not 32 since 40-6 is 34.

[@ashokkumarkalme1839]

Yes

[@taesthetic22]

Finally ye chapter bhi ho gya 😊

[@AshvakKhan-x9r]

Sacch mein is sir ko salam 😢 wow wtt a teaching fulll chapter understood sir 😊 world best maths teacher😊😊

[@Arnav_189]

2:52:06 - (i) 7 + 10 ½ + 14 + .... + 84 = 1046 ½ 2:54:15- (ii) 34 + 32 + 30 + .... + 10 = 286 2:56:22 - (iii) - 5 + (- 8) + (- 11) + .... + (- 230) = - 8930 2:59:21- = 440 3:01:57 There is a calculation mistake, d will be 7/3 and not 5/2 = 273 3:34:23 - Sum of the first n terms of an AP is given by Sn = n/2 [2a + (n - 1) d] or Sn = n/2 [a + l] Here, a is the first term, d is the common difference, n is the number of terms and l is the last term. Given, First term, a = 9 Common difference, d = 17 - 9 = 25 - 17 = ... = 8 Sum up to nth terms, Sn = 636 We know that sum of n terms of an AP Sn = n/2 [2a + (n - 1) d] 636 = n/2 [2 × 9 + (n - 1) 8] 636 = n/2 [18 + 8n - 8] 636 = n/2 [10 + 8n] 636 = n[5 + 4n] 636 = 5n + 4n2 4n2 + 5n - 636 = 0 4n2 + 53n - 48n - 636 = 0 n (4n + 53) - 12 (4n + 53) = 0 (4n + 53)(n - 12) = 0 Either 4n + 53 = 0 or n - 12 = 0 n = - 53/4 or n = 12 n cannot be -53/4 because the number of terms can neither be negative nor fractional, therefore, n = 12 3:45:30 = 6973 3:47:38 =1661 3:49:21 =5610 3:58:12- (i) aₙ = 3 + 4n Given, nth term, aₙ = 3 + 4n a₁ = 3 + 4 × 1 = 7 a₂ = 3 + 4 × 2 = 3 + 8 = 11 a₃ = 3 + 4 × 3 = 3 + 12 = 15 a₄ = 3 + 4 × 4 = 3 + 16 = 19 It can be observed that a₂ - a₁ =11 - 7 = 4 a₃ - a₂ =15 - 11 = 4 a₄ - a₃ =19 - 15 = 4 So, the difference of aₙ and aₙ₋₁ is constant. Therefore, this is an AP with common difference as 4 and first term as 7. The sum of n terms of AP is given by thre formula Sₙ = n/2 [2a + (n - 1) d] Sum of 15 terms, S₁₅ = 15/2 [2 × 7 + (15 - 1) 4] = 15/2 [14 + 14 × 4] = 15/2 × 70 = 15 × 35 = 525 (ii) aₙ = 9 - 5n Given, nth term is aₙ = 9 - 5n a₁ = 9 - 5 × 1 = 9 - 5 = 4 a₂ = 9 - 5 × 2 = 9 - 10 = - 1 a₃ = 9 - 5 × 3 = 9 - 15 = - 6 a₄ = 9 - 5 × 4 = 9 - 20 = - 11 It can be observed that a₂ - a₁ = (-1 ) - 4 = - 5 a₃ - a₂ = (-6) -(-1) = - 5 a₄ - a₃ = (- 11) - (- 6) = - 5 So, the difference of aₙ and aₙ₋₁ is constant. Therefore, this is an A.P. with common difference - 5 and first term as 4. The sum of n terms of AP is given by thre formula Sₙ = n/2 [2a + (n - 1) d] S₁₅ = 15/2 [2 × 4 + (15 - 1)(- 5)] = 15/2 [8 + 14 (- 5)] = 15/2 [8 - 70] = 15/2 × (- 62) = - 465 4:07:18- The sum of the first n terms of an AP is given by Sₙ = n/2 [2a + (n - 1) d] or Sₙ = n/2 [a + l], and the nth term of an AP is aₙ = a + (n - 1)d Here, a is the first term, d is the common difference and n is the number of terms and l is the last term. The positive integers that are divisible by 6 are 6, 12, 18, 24, ... It can be observed that these numbers are forming an AP. Hence, First term, a = 6 Common difference, d = 6 Number of terms, n = 40 As we know that sum of n terms is given by the formula Sₙ = n/2 [2a + (n - 1) d] S₄₀ = 40/2 [2 × 6 + (40 - 1)6] = 20 [12 + 39 × 6] = 20 [12 + 234] = 20 × 246 = 4920 4:08:25- The sum of the first n terms of an AP is given by Sₙ = n/2 [2a + (n - 1) d] or Sₙ = n/2 [a + l] Here, a is the first term, d is a common difference and n is the number of terms. The multiples of 8 are 8, 16, 24, 32, ... These numbers are in an A.P. Hence, First term, a = 8 Common difference, d = 8 Number of terms, n = 15 As we know that sum of n terms is given by the formula Sₙ = n/2 [2a + (n - 1) d] S₁₅ = 15/2 [2 × 8 + (15 - 1)8] = 15/2 [16 + 14 × 8] = 15/2 [16 + 112] = 15/2 × 128 = 15 × 64 = 960 4:12:07- The sum of the first n terms of an AP is given by Sₙ = n/2 [2a + (n - 1) d] or Sₙ = n/2 [a + l]. Here, a is the first term, d is a common difference and n is the number of terms. The odd numbers lying between 0 and 50 are 1, 3, 5, 7, 9 ... 49 Therefore, it can be observed that these odd numbers are in an A.P. Hence, First term, a = 1 Common difference, d = 2 Last term, l = 1 We know that nth term of AP, aₙ = l = a + (n - 1)d 49 = 1 + (n - 1) 2 48 = 2(n - 1) n - 1 = 24 n = 25 We know that sum of n terms of AP, Sₙ = n/2 [a + l] S₂₅ = 25/2 (1 + 49) = 25/2 × 50 = 25 × 25 = 625 4:16:30 - Sₙ = n/2 [2a + (n - 1) d] S₃₀ = 30/2 [2 × 200 + (30 - 1) 50] = 15 [400 + 1450] = 15 × 1850 = 27750 4:34:38- S₁₃ = 13/2 [2 × (0.5π) + (13 - 1)(0.5π) ] = 13/2 [ π + 6π] = 13/2 × 7π = 13/2 × 7 × 22/7 (By taking π = 22/ 7) = 143 4:50:27- Distance of 10 potatoes from the bucket is such that, the first potato is 5m away from the bucket and other potatoes are placed 3m apart in a straight line. To find the total distance the competitor has to run, we will find the sum of the AP if they are in an arithmetic Progression The sum of the first n terms of an Arithmetic Progression is given by Sₙ = n/2 [2a + (n - 1) d]. Here, a is the first term, d is a common difference and n is the number of terms. The distances of potatoes are as follows. 5, 8, 11, 14, ... It can be observed that these distances are in A.P. First term, a = 5 Common difference, d = 8 - 5 = 3 Number of terms, n = 10 We know that the sum of n terms is given by the formula Sₙ = n/2 [2a + (n - 1) d] S₁₀= 10/2 [2 × 5 + (10 - 1) × 3] = 5 [10 + 27] = 5 × 37 S₁₀ = 185 Like every time she has to run back to the bucket, therefore, the total distance that the competitor has to run will be two times the total distance. Therefore, the total distance that the competitor will run = 2 × 185 m = 370 m Alternatively, The distances of potatoes from the bucket are 5, 8, 11, 14... The distance run by the competitor for collecting these potatoes is two times the distance at which the potatoes have been kept. Therefore, distances to be run are First potato, a = 2 × 5m =10m Second potato, a₂ = 2 × (5 + 3) m = 16m Third potato, a₃ = 2 × (5 + 2 × 3) m = 22m Number of potatoes, n = 10 10, 16, 22, 28, 34,.... a = 10 d = 16 - 10 = 6 Sₙ = n/2 [2a + (n - 1) d] = 10/2 [2 × 10 + (10 - 1)6] = 5[20 + 54] = 5 × 74 = 370 5:46:30 - The sum of the first n terms of an AP is given by Sₙ = n/2 [2a + (n - 1) d], where a is the first term, d is a common difference and n is the number of terms. From the figure, it can be observed that the Height of 1st step is ¼ m Height of the 2nd step is (¼ + ¼) m = ½ m Height of 3rd step is (¼ + ¼ + ¼) m = 3/4 m Therefore, the height of each step is increasing by ¼ m Length 50m and width (tread) is the same for each step that is ½ m Volume of step can be considered as Volume of Cuboid = length × breadth × height Volume of concrete in 1st step = 50m × ½ m × ¼ m = 6.25 m³ Volume of concrete in 2nd step = 50m × ½ m × ½ m = 12.50 m3 Volume of concrete in 3rd step = 50m × ½ m × ¾ m = 18.75 m3 It can be observed that the volumes of concrete in these steps are in an A.P.: 6.25m³, 12.50m³, 18.75m³, .... First term a = 6.25, Common difference d = 6.25 Let nth term of AP be the 15th value since number of steps = 15 Sum of n terms, Sₙ = n/2 [2a + (n - 1) d] S₁₅ = 15 / 2 [2 × 6.25 + (15 - 1) × 6.25] = 15 / 2 [12.50 + 14 × 6.25] = 15 / 2 [12.50 + 87.50] = 15/2 × 100 = 750 m³ Therefore, the volume of concrete required to build the terrace is 750 m³. MORE HOMEWORK I WILL WRITE I HAVE NO TIME I AM RAJASTHAN CRICKET PLAYER

[@vermadiwakar0.7]

Chatgpt

[@radhikayadav4673]

Fantastic yrrr thanks last question solve ni ho ra tha to ab samj a gaya dear keep it up ❤

[@aszfact44966]

Oo bhai topper ho kiya❤

[@DARK-lh3qn]

3:18:38. → a5=34 (not 32)

[@shivaniojha24]

Yeah 👍🏻

[@antrasingh9757]

55:11 ye ap h iski common difference 24 h aur ncert k ans me v ye ap h so yhi thodi se mistake hue h by the way thankyou so much sir😊❤