Question

Find the sum of all two-digit numbers which give a remainder of 3 when they are divided by 7.

Answer 1

The two digit number which gives a remainder of $3$ when divided by $7$ are:
$10,17,24.....94$

Now, these number are in AP series with
1st Term, $a=10$
Number of Terms, $n=13$
Last term, L = 94 and
Common Difference $d=7$
Sum $=n\times \frac{(a+L)}{2}$
$=13\times 52=676$.