SOLUTION: The sum of 40 consecutive integers is 100 what is the largest integer

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Question 561862: The sum of 40 consecutive integers is 100 what is the largest integer
Answer by Edwin McCravy(20056) About Me  (Show Source):
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The sum of 40 consecutive integers is 100 what is the largest integer
The largest integer is the 40th term, or a40

Consecutive integers form an arithmetic sequence with a common difference of 1.

This is an aritmetic series with n=40 terms and S40 = 100

The formulas we will use are:

Sn = n%2F2[2a1 + (n-1)d] and an = a1 + (n-1)d

where n = 40, Sn = S40 = 100, d=1

S40 = 40%2F2[2a1 + (40-1)·1]

100 = 20[2a1 + 39·1]

100 = 20[2a1 + 39]

Divide both sides by 20

5 = 2a1 + 39

-34 = 2a1

-17 = a1

The largest integer is the 40th term a40

an = a1 + (n-1)d
a40 = -17 + (40-1)·1
a40 = -17 + 39·1
a40 = -17 + 39
a40 = 22

The largest term is 22.

-17-16-15-14-13-12-11-10-9-8-7-6-5-4-3-2-1+0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22 = 100

Edwin