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anonymous

  • one year ago

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

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  1. anonymous
    • one year ago
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    HI! I can help you!

  2. anonymous
    • one year ago
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    Have you seen this sort of sequence before?

  3. anonymous
    • one year ago
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    Not really

  4. anonymous
    • one year ago
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    Okay, cool. Just to help me know how to approach the problem, what have you guys been studying in class recently?

  5. anonymous
    • one year ago
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    geometric sequences

  6. anonymous
    • one year ago
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    I don't really understand how to find the sum of a sequence though

  7. anonymous
    • one year ago
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    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).

  8. anonymous
    • one year ago
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    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?

  9. anonymous
    • one year ago
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    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

  10. anonymous
    • one year ago
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    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!

  11. anonymous
    • one year ago
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    so then what's the "magic" formula

  12. anonymous
    • one year ago
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    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

  13. anonymous
    • one year ago
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    (If you don't have headphones/speakers then I can explain, of course - let me know if you prefer that option!)

  14. anonymous
    • one year ago
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    okay thank you! in the mean time can you tell me how to find the sum?

  15. anonymous
    • one year ago
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    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?

  16. anonymous
    • one year ago
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    (Let's see if I beat the 7 minute video!)

  17. anonymous
    • one year ago
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    sure!

  18. anonymous
    • one year ago
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    Okay, I get \[n(\frac{ 2a+(n-1)d }{ 2 })\]

  19. anonymous
    • one year ago
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    Hmm, 7 minutes. Looks like I pretty much tied with the video :P

  20. anonymous
    • one year ago
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    so the n would be 9 right? what about the a or d

  21. anonymous
    • one year ago
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    Yep!

  22. anonymous
    • one year ago
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    Well, "a" is the first number, so 2 in your case.

  23. anonymous
    • one year ago
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    And "d" is the difference between the terms, which is -9 (since you're subtracting 9 each time)

  24. anonymous
    • one year ago
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    Does that make sense at all? :)

  25. anonymous
    • one year ago
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    yes perfect sense thank you!

  26. anonymous
    • one year ago
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    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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