What is the sum of the first 8 terms of the series: -2 + 4 - 6 + 8 - 10 + ... ?

Question

goformit100 · Answer

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terenzreignz · Answer

This is no arithmetic progression... -.-

terenzreignz · Answer

You just have to see the trend, it would seem...

goformit100 · Answer

Sorry Sir

anonymous · Answer

the ans is 8

terenzreignz · Answer

That is is... but how'd you arrive at it?

terenzreignz · Answer

*That it is*

anonymous · Answer

i just simply added the terms............but i cant find an absolute mathmaticl process for it............

jhannybean · Answer

This series is alternating,we know that. Because the numbers ALTERNATE between positives and negatives, what else do we know?

hartnn · Answer

break it into 2 series, 
-2, -6,-10.....
4,8,.....
now both are arithmatic sequences!

jhannybean · Answer

Weknow that there is a common "increasing factor"

jhannybean · Answer

lolwth @hartnn  haha

terenzreignz · Answer

Or just note that every two terms, you get a sum of 2
-.-
So since there would be 4 sets of two consecutive terms, you get 4 times 2 which is 8

hartnn · Answer

of you wanna show a method, i suggest, you break the sequence into 2 sequences, find the sum of first 4 terms of both the sequences,. then add them to get sum of 1st 8 terms

jhannybean · Answer

$$\sum_{n=1}^{\infty}(-1)^{n-1}\dots$$