Question

Find the sum of the first 9 terms of the sequence.
2, -7, -16, -25, ...

Answer 1

HI! I can help you!

Answer 2

Have you seen this sort of sequence before?

Answer 3

Not really

Answer 4

Okay, cool. Just to help me know how to approach the problem, what have you guys been studying in class recently?

Answer 5

geometric sequences

Answer 6

I don't really understand how to find the sum of a sequence though

Answer 7

Okay, I can help you with that! First of all, I think in this case we've got an arithmetic sequence rather than a geometric one, since we're adding (or subtracting) to get from one number to the next, rather than multiplying (or dividing).

Answer 8

There's a (magic) formula to find the sum of an arithmetic sequence. Would you like me to just remind you of the formula, or would you like to see where it comes from?

Answer 9

u find the pattern between the numbers given and then continue the sequence like for this problem the pattern is u subtract 9 u keep doing that until u have nine terms counting the ones u already got and the add them all together

Answer 10

What @Player_2 suggested is one possible way, but it's not the fastest. Imagine if you had to add up 100 numbers rather than 9: it would take forever if you did it one-by-one!

Answer 11

so then what's the "magic" formula

Answer 12

Okay I was going to type out an expanation, but actually I think it'll just be faster if you watch this Youtube video. It's 7 minutes long, which is less time than I'd spend explaining it :) Here's the link: https://youtu.be/Uy_L8tnihDM

Answer 13

(If you don't have headphones/speakers then I can explain, of course - let me know if you prefer that option!)

Answer 14

okay thank you! in the mean time can you tell me how to find the sum?

Answer 15

To be honest, I'll have to work out the formula myself :) You start watching the video, and I'll let you know once I've worked it out. Does that work for you?

Answer 16

(Let's see if I beat the 7 minute video!)

Answer 17

sure!

Answer 18

Okay, I get \[n(\frac{ 2a+(n-1)d }{ 2 })\]

Answer 19

Hmm, 7 minutes. Looks like I pretty much tied with the video :P

Answer 20

so the n would be 9 right? what about the a or d

Answer 21

Yep!

Answer 22

Well, "a" is the first number, so 2 in your case.

Answer 23

And "d" is the difference between the terms, which is -9 (since you're subtracting 9 each time)

Answer 24

Does that make sense at all? :)

Answer 25

yes perfect sense thank you!

Answer 26

No problem! If you get stuck on any similar problems, I find the Khan Academy website really useful. It'll show you a video explaining the idea, and then let you try exercises, and I think it even works through the answers if you get stuck! https://www.khanacademy.org/math/integral-calculus/sequences_series_approx_calc/calculus-series/v/formula-for-arithmetic-series