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

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

Mathematics
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HI! I can help you!
Have you seen this sort of sequence before?
Not really

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Other answers:

Okay, cool. Just to help me know how to approach the problem, what have you guys been studying in class recently?
geometric sequences
I don't really understand how to find the sum of a sequence though
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).
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?
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
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!
so then what's the "magic" formula
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
(If you don't have headphones/speakers then I can explain, of course - let me know if you prefer that option!)
okay thank you! in the mean time can you tell me how to find the sum?
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?
(Let's see if I beat the 7 minute video!)
sure!
Okay, I get \[n(\frac{ 2a+(n-1)d }{ 2 })\]
Hmm, 7 minutes. Looks like I pretty much tied with the video :P
so the n would be 9 right? what about the a or d
Yep!
Well, "a" is the first number, so 2 in your case.
And "d" is the difference between the terms, which is -9 (since you're subtracting 9 each time)
Does that make sense at all? :)
yes perfect sense thank you!
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

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