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

Question

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

mehek14 · Answer

what do you think?

anonymous · Answer

i have no idea on how to do this

jhannybean · Answer

Iwould start with b, seems a bit easier.

jhannybean · Answer

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 · Answer

it decreases by ten

jhannybean · Answer

I've got to head off for a bit, I'll get someone on to help you @Michele_Laino please? Thank you !

mehek14 · Answer

yes it does decrease by 10 each time

mehek14 · Answer

how about in A?

anonymous · Answer

by 7?

mehek14 · Answer

increase or decrease

anonymous · Answer

increasing

mehek14 · Answer

correct

anonymous · Answer

what's next?

loser66 · Answer

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 · Answer

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 · Answer

Imitate the same process to get the answer for b) instead of +7, you do -10