SOLUTION: 1.Find the sum of the even integers between -24 and 226, including end numbers.

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Question 1151999: 1.Find the sum of the even integers between -24 and 226, including end numbers.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The series which we want to add can be given as :

-24,-22,-20,........,224,226

Sum of N numbers in AP is given by:

S%5Bn%5D=n%28a%2Bl%29%2F2 ........where, a = First element in AP,+l = Last element in AP

According to the series we have number of total elements n+which can be calculated as:

l=a%2B%28n-1%29d, where n = number of elements.

in your case l=226, a=-24,d=2

l=a%2B%28n-1%29d
226=-24%2B%28n-1%292
226%2B24=%28n-1%292
250%2F2=n-1
125=n-1
125%2B1=n
n=126

now we can find the sum:
S%5Bn%5D=n%28a%2Bl%29%2F2.....substitute n,a, and l
S%5B126%5D=126%28-24%2B226%29%2F2
S%5B126%5D=126%28202%29%2F2
S%5B126%5D=12726