7, 11, 15, 19, …, what is the 100th term of this arithmetic sequence?

How to find the nth term formula of an arithmetic sequence and find the value of a term.
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[@bendono]

I do not know that formula, so I did the following. 1) realize that the formula must have a constant slope, 2) calculate slope as (y2 - y1) / (x2 - x1) --> (11 - 7) / (2 - 1) --> 4, 3) integrate the slope to obtain the formula --> f(x) = 4x + C, 4) plug in any (x,y) and solve for C --> f(x) = 4x + 3. For 3) you can also just use "y = mx + b" instead of integration; it's all the same in the end.

[@83emthomas]

Thank you thank you thank you. Back in school after a long break

[@tomtke7351]

It would seem numbers advance, one to the next by 4. start is 7 2nd number is 7 + 4 = 11 3rd number is 7 + 4 + 4 = 15 4th number is 7 + 4 + 4 + 4 = 19 nth number = 7 + (4 × (n - 1)) 100th => 7 + (4 × (100 - 1)) = 7 + (4 × 99) = 7 + 396 = 403 Rethink => the number of steps BETWEEN 100 numbers is 99 Each step is 4 99 × 4 = 396 weighted steps between 7 and the 100th number. start is 7 so finish is 7 + 396 = 403✔️ After watching video I see a different formula: mine is 7 + ( (n - 1) × 4) which is also 3 + 4 + ((n -1)×4) = 3 + 4n ✔️

[@GoBlesstheSky]

Oh yeah, I went with, 4th number of 100 is 19 so.. 19+(4X96)=403

[@danieldennis9831]

It's 403. The sequence is the base + multiples of 4. Base+differnce(sequence number-1). It would be harder with a geometric progression to come up with an equation. Took 20 seconds with this one.

[@argonwheatbelly637]

403 in about eight seconds in my head, but I like the approach in the video.

[@lisanelson3260]

What is the 100th 1, 4, 7, 10

[@michaelempeigne3519]

403

[@nicoladwyer9541]

403 because rule 4n+3

[@kk6aw]

399 starting at zero

[@pradipeditor]

Hi

[@16lrrr54]

lil yapper ay

[@helpme-zk7ul]

less talking more working. I litteraly wasted 8 mins hearing ur introduction

[@monzinox7384]

you talk to much mate just get to the point

[@dwaipayandattaroy9801]

123

[@mawavoy]

407

[@richardodell]

403

[@colintwigger529]

No wonder some students can’t understand maths . I explained this and other more complicated number series to my students and the all understood in a few minutes.

[@donmoroz5502]

403

[@donmoroz5502]

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