UPSC 2014 CDS II Math Paper

Two digit positive integers less than 50, which when divided by 4 leaves the remainder 1 are 13, 17, 21,..., 49.
These numbers are in AP witha = 13 and d = 4.
Let 49 be the nth term of the AP.
13+(n−1)×4=49
⇒n−1=

36

4

=9⇒n=10
∴ Sum of the number =

10

2

(13+49)
=5×62[S=

n

2

(a+I)]=310