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

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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what do you think?
i have no idea on how to do this
Iwould start with b, seems a bit easier.

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Other answers:

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

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