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)   (Show Source): You can put this solution on YOUR website!
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 = [2a1 + (n-1)d] and an = a1 + (n-1)d

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

S40 = [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
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