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anonymous

  • one year ago

what is a summation notation for the series? a. -5 +2+9+16+...+261+268 b. 500+490+480+...+20+10

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  1. Mehek14
    • one year ago
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    what do you think?

  2. anonymous
    • one year ago
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    i have no idea on how to do this

  3. Jhannybean
    • one year ago
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    Iwould start with b, seems a bit easier.

  4. Jhannybean
    • one year ago
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    This is what you call an arithmetic sequence, where you have a common `difference` between the numbers in a sequence. Can you spot what the difference is?

  5. anonymous
    • one year ago
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    it decreases by ten

  6. Jhannybean
    • one year ago
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    I've got to head off for a bit, I'll get someone on to help you @Michele_Laino please? Thank you !

  7. Mehek14
    • one year ago
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    yes it does decrease by 10 each time

  8. Mehek14
    • one year ago
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    how about in A?

  9. anonymous
    • one year ago
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    by 7?

  10. Mehek14
    • one year ago
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    increase or decrease

  11. anonymous
    • one year ago
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    increasing

  12. Mehek14
    • one year ago
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    correct

  13. anonymous
    • one year ago
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    what's next?

  14. Loser66
    • one year ago
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    For a) \(a_2= a_1+7\\a_3= a_2+7= a_1+2*7\\a_4=a_3+7 = a_1+3*7\\--------------\\a_n= a_1+(n-1)7\)

  15. Loser66
    • one year ago
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    Now, calculate the last term: \(268 = a_1 +(n-1) 7=-5 +(n-1) *7\) solve for n, you have n= 40 Hence the summation is \[\sum_{n=1}^{40} -5+7(n-1)\]

  16. Loser66
    • one year ago
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    Imitate the same process to get the answer for b) instead of +7, you do -10

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