SOLUTION: What is the sum of all the integers between 40 and 440 which end in 3?

Question 1191494: What is the sum of all the integers between 40 and 440 which end in 3?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The numbers are 43, 53, 63, ..., 423, and 433. They form an arithmetic sequence with common difference 10.

The sum of the terms of an arithmetic sequence is (number of terms) times (average of terms). And in an arithmetic sequence, the average of all the terms is the average of the first and last.

For this problem, the average is (43+433)/2 = 476/2 = 238.

The number of terms is (last term minus first term), divided by the common difference, plus 1. Note you need the "plus 1" because the other part of the calculation determines the number of terms AFTER THE FIRST ONE.

For this problem, the number of terms is ((433-43)/10)+1 = (390/10)+1 = 39+1 = 40.

The sum of the terms is then 40(238) = 9520.

ANSWER: 9520

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