SOLUTION: what is the sum of all integers between -25 and +26

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Question 637371: what is the
sum of all integers between -25 and +26
Found 2 solutions by Tatiana_Stebko, ewatrrr:
Answer by Tatiana_Stebko(1539) About Me  (Show Source):
You can put this solution on YOUR website!
The sum is 26
because -25+25=0
-24+24=0 etc
-25%2B%28-24%29%2B%28-23%29%2B...+%2B23%2B24%2B25%2B26=%28-25%2B25%29%2B%28-24%2B24%29%2B%28-23%2B23%29%2B...+%2B%28-1%2B1%29%2B0%2B26=26

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

{-25, ...26}  Arithemetic Sequence, d = 1  and a%5B1%5D+=+-25

a%5Bn%5D+=+-25+%2B+%28n-1%29+=+26,   n = 52

S%5Bn%5D=%28n%28a%5B1%5D%2Ba%5Bn%5D%29%29%2F2

S%5B52%5D=+%2852%28-25+%2B+26%29%29%2F2+=+26+

0r

S%5Bn%5D=%28n%2F2%29%282%2Aa%5B1%5D%2B+%28n-1%29d%29

S%5B52%5D=%2826%29%28-50%2B+%2851%29%2A1%29=+26