Harmonic Mean Between Two Terms | Math Corner

[@flickergaming1803]

hi! pwede po bang magtanong kung anong software ginagamit niyo for your slide?

[@mathcorner]

Hello Isaac. I used ppt.

[@WCWFO]

Hi sir how do u answer this one Insert three harmonic means between 2 1/2 and-2 1/2?

[@mathcorner]

@@WCWFO if it is a mixed number, convert in improper fraction.

[@WCWFO]

@@mathcorner thank you sir!

[@nilleytchl1105]

Can you try to solve this sir its quite hard for me tho What term of the harmonic sequence whose second and fourth terms are respectively, 1/14 and 1/12 is undefined?

[@mathcorner]

Hi Nille YtChl 😊 You are asked to determine which term is 1/0 (which is undefined). 2nd term is 1/14 4th term is 1/12 6th term is 1/10 8th term is 1/8 ... Which term is 1/0? 😊 Kindly share this to your friends and classmates. Thanks 😊

[@nilleytchl1105]

ty sir, I'll share this to my friends✨

[@mathcorner]

@@nilleytchl1105thanks 😊

[@jeraldinecanaveral3902]

Ser what if, Insert the stated harmonic means: Two terms; between 6 and 32.

[@mathcorner]

Hello FIGHTING STARS. Let the first term equal to 6 and the fourth term equal to 32. Harmonic Seq. 6, __, __, 32 Arithmetic Seq. 1/6, __, __, 1/32. Kind share this to your friends and classmates. Thanks 😊

[@meckbryanteyana6207]

how did you get 5-1 in finding the common difference? im confuse ... please reply

[@mathcorner]

Fifth term and first term. That is a shortcut method in finding the common difference. For instance, first term is 7 and fifth term is 19, d = (19-7)/(5-1) = 12/4 =3

[@tutingrubena1584]

wow 👏👏

[@emmanuelreyes6724]

@@mathcorner ur rlly not clear on your explanation sometimes sir, so it becomes confusing too..

[@mathcorner]

@@emmanuelreyes6724 in which part?

[@roseanndacanay1052]

4 harmonic means between 5/31 and 5/106

[@mathcorner]

Hello Rose Ann Dacanay 😊 The reciprocal of 5/31 is 31/5 and the reciprocal of 5/106 is 106/5. It means that 31/5, __, __, __, __, 106/5 is an arithmetic sequence. First, solve for d. You may use d = (a6 - a1)/(6-1) in finding the common difference. Next, find the a2 by adding a1 and d, a3 by adding a2 and d, and so on. Finally, find the reciprocal of each arithmetic mean.

[@roseanndacanay1052]

Thaaankkk youuu. Much appreciated 😊

[@mathcorner]

@@roseanndacanay1052 you're very welcome 😊

[@mlplayer9097]

How did you get the 8/6?

[@mathcorner]

4/3 multiply by 2/2 = 8/6

[@Majiqq_38]

Math Corner where to get 2/2?

[@mathcorner]

@@Majiqq_38 since we will convert 4/3 to a fraction where the denominator is equal to 6, we need to multiply by 2. If we multiply 2 to the denominator, we also need to multiply 2 to the numerator. Kindly share this channel to your friends and classmates. Thanks 😊

[@Majiqq_38]

Math Corner sure because this is our lesson today hehehe ty for explaining 😁

[@mathcorner]

@@Majiqq_38 you are welcome. If you have more questions, just comment here 😊

[@Rosee_CJ]

where did you get the 32/24😭

[@mathcorner]

Convert 4/3 to a fraction where the denominator is equal to 24. To do that, multiply 4/3 by 8/8.

[@GloriaRodriguez-z6t]

​@@mathcornerI understood that you got 24 but how did you get the 32?

[@mathcorner]

@@GloriaRodriguez-z6t multiply the numerator by the numerator, 4 x 8 = 32.

[@oneonety1ne]

2:02 how, where did 1 over 4 come from

[@tutingrubena1584]

1:28 what is 5 - 1 ?? where did it came from?

[@mathcorner]

Fifth term and first term 😊

[@allmycryptoes9885]

where'd you edit videos?

[@mathcorner]

Application? I used ppt.

[@vctorludorum9047]

Anong equation ginamit niyo dyan?

[@mathcorner]

@@vctorludorum9047 the reciprocal of the terms of harmonic sequence will form an arithmetic sequence. First step is to write the reciprocals, and then, use the formula for the nth term of arithmetic sequence.

[@WertgTuu]

pano po pag: one between a and b?

[@mathcorner]

@@WertgTuu same method. Find the reciprocals of a and b, to become arithmetic sequence. Next, find the arithmetic mean of a and b. Finally, find the reciprocal of the arithmetic mean.

[@ahkr1102]

sir hindi po ba gagawing mixed number pag imporper fraction sya?

[@mathcorner]

Hi Angel. Pwedeng gawing mixed number. Pwede din na improper fraction. Kindly share this video to your friends and classmates. Thanks 😊

[@nadinepalad7761]

hi sir are u a filipino ask ko lang po pano kung ang given number ay 3 and 9 pano po makukuha yung common ratio nila

[@mathcorner]

Hello Nadine Palad 😊 Is the given sequence geometric? Which term is 3 and which term is 9?

[@paloytzy8115]

Hi sir please help po What is the Three terms between 1/100 and 1/212 to form a harmonic sequence of five terms?

[@paloytzy8115]

5 hours ko napong sinosolve di kona na kuha hehe please help po

[@mathcorner]

@@paloytzy8115 first, make them arithmetic sequence. Since the first and fifth terms of harmonic sequence are 1/100 and 1/212, respectively, the first and fifth terms of the arithmetic sequence are 100 and 212, respectively. Next step, determine the common difference of the arithmetic sequence if its first term is 100 and its fifth term is 212.

[@paloytzy8115]

@@mathcorner thank you sir may your channel grow more ❤

[@mathcorner]

@@paloytzy8115 you are welcome 😊

[@paloytzy8115]

Ahmm sorry sir but how to determine the common difference of an arithmetic sequence if its first and fifth term please help me with this sir

[@KimSunoo2403]

What if there is no term indicated?

[@mathcorner]

Hello Justin. The number of terms to be inserted is not indicated? Or is it asking for harmonic mean? If it is asking for harmonic mean, then you have to insert one term between the two given terms.

[@Majiqq_38]

Is it always 5-1? In the easiest way to get the common diff?

[@mathcorner]

No. The reason why it is 5 - 1 because the given terms are 5th term and 1st term.

[@Majiqq_38]

Math Corner can you tell me what is the shortcut way to get the answer for the Harmonic means?

[@mathcorner]

@@Majiqq_38 just remember that the reciprocals of the terms of harmonic sequence form an arithmetic sequence. After finding the terms of arithmetic sequence, you can use the shortcut in finding the common difference to easily determine the arithmetic means. After finding arithmetic means, find the reciprocals to determine the harmonic means. If there is only one term missing, the formula is included in this video.

[@Majiqq_38]

Math Corner thank you so much😁

[@mathcorner]

@@Majiqq_38 you are welcome 😊

[@julianablanca9571]

How about 3,_,_,_,9 sir?

[@mathcorner]

Hello Juliana Blanca 🙂 The reciprocal of the terms form an arithmetic sequence. If 3, __, __, __, 9 is harmonic seq, 1/3, __, __, __, 1/9 is arithmetic seq. You have to find the common difference. Use d = (a5-a1)/(5-1). After that, a2 = a1 + d a3 = a2 + d a4 = a3 + d And then, find the reciprocal 🙂

[@mr.notuploadanylonger2232]

2:52 is it multiplication!? Actually, 4x7 = 28. Not 32. If i was correct. EDIT THIS VIDEOS NOW

[@mathcorner]

4/3 = 32/24 Equivalent fraction. To convert 4/3 into fraction where the denominator is 24, Multiply 8 to numerator and denominator. (4x8)/(3x8)=32/24

[@mr.notuploadanylonger2232]

OK i understand

[@taikoateurparents1128]

@@mathcorner where did 8 come from?

[@mathcorner]

@@taikoateurparents1128 In 4/3, the denominator is 3. To convert 4/3 in a fraction where the denominator is 24, we need to multiply the numerator and denominator by 8. Another way, 4/3 = x/24. Divide the denominators, 24÷3=8. Multiply to the numerator, (8)(4)=32. 4/3=32/24

[@taikoateurparents1128]

@@mathcorner what if the first term is 1/3 and the 5 term is 1/9?

[@reina_harhar7815]

What if there's 4 terms? 1/4,__, __, 1/9?

[@mathcorner]

In the harmonic sequence, the first term is 1/4 and the fourth term is 1/9. It means that the first term of arithmetic sequence is 4 and the fourth term is 9. To find the two missing terms between them, use the formula for the nth term (an = a1 + (n-1)d) of arithmetic sequence.

[@123-k5t]

Pahelp po. Find the harmonic mean between 2 and 1/8

[@mathcorner]

Hello Jayson Aguinaldo 😊 Since there is only one term between 2 and 1/2, you may use the formula 2ab/(a + b). Consider the following examples. Example 1 5:00 Example 2 Insert harmonic mean bet. 3 and 1/4. Solution 2ab/(a+b) 2(3)(1/4) / (3 + 1/4) Since 2(3)(1/4) = 6/4 = 3/2 and 3 + 1/4 (3 = 3/1 = 12/4) = 12/4 + 1/4 = 13/4. 2(3)(1/4) / (3 + 1/4) becomes (3/2) / (13/4) = (3/2)(4/13) = 12/26 = 6/13

[@queenymlbestplay9856]

2×(1/6)(1/3) = 2/18 =1/9

[@mathcorner]

You are correct, Queeny ML 😊 2/18 in lowest term is 1/9. Since, 3/6 = 1/2, 2/18 ÷ 3/6 is also equal to 1/9 ÷ 1/2, which is equal to 2/9.

[@HAmuu97]

Welcome Hababi Come to Dubai

[@amyayag3588]

mathcorner diko gets

[@YYYUP62X]

are u from Russia ..

[@mathcorner]

No Yash