UPSC 2015 CDS II Math Paper

The two-digit positive numbers, which when divided by 7 leave remainder 3, are 10, 17, 24, ..., 94.
These numbers are in AP with a = 10 and d = 7.
Suppose 94 is the nth term of the AP.
∴an=a+(n−1)d=94
⇒10+(n−1)×7=94
⇒n−1=

84

7

=12
⇒n=13
Therefore, the required sum
=

n

2

(a+I)=

13

2

×(10+94)
=

13

2

×104=676