Progresssions  AP, GP, HP  CAT 2016
Question 4 the day : April 17, 2006
The question for the day is a sample practice problem in Sequences and series  AP and summation of terms of an AP. This question appeared in CAT 2003.
Question
What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3?
 897
 164,850
 164,749
 149,700
Correct Choice is (2) and Correct Answer is 164,850.
Explanatory Answer
The smallest 3 digit number that will leave a remainder of 2 when divided by 3 is 101.
The next number that will leave a remainder of 2 when divided by 3 is 104, 107, ....
The largest 3 digit number that will leave a remainder of 2 when divided by 3 is 998.
So, it is an AP with the first term being 101 and the last term being 998 and common difference being 3.
Sum of an AP =
We know that in an A.P., the nth term a _{n} = a _{1} + (n  1)*d
In this case, therefore, 998 = 101 + (n  1)* 3
i.e., 897 = (n  1) * 3
Therefore, n  1 = 299
Or n = 300.
Sum of the AP will therefore, be = 164,850
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