anonymous
  • anonymous
what is a summation notation for the series? a. -5 +2+9+16+...+261+268 b. 500+490+480+...+20+10
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Mehek14
  • Mehek14
what do you think?
anonymous
  • anonymous
i have no idea on how to do this
Jhannybean
  • Jhannybean
Iwould start with b, seems a bit easier.

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Jhannybean
  • Jhannybean
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?
anonymous
  • anonymous
it decreases by ten
Jhannybean
  • Jhannybean
I've got to head off for a bit, I'll get someone on to help you @Michele_Laino please? Thank you !
Mehek14
  • Mehek14
yes it does decrease by 10 each time
Mehek14
  • Mehek14
how about in A?
anonymous
  • anonymous
by 7?
Mehek14
  • Mehek14
increase or decrease
anonymous
  • anonymous
increasing
Mehek14
  • Mehek14
correct
anonymous
  • anonymous
what's next?
Loser66
  • Loser66
For a) \(a_2= a_1+7\\a_3= a_2+7= a_1+2*7\\a_4=a_3+7 = a_1+3*7\\--------------\\a_n= a_1+(n-1)7\)
Loser66
  • Loser66
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 \[\sum_{n=1}^{40} -5+7(n-1)\]
Loser66
  • Loser66
Imitate the same process to get the answer for b) instead of +7, you do -10

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