Question:
Sum of all two digit numbers which when divided by 4 yield unity as remainder is
(a) 1200
(b) 1210
(c) 1250
(d) none of these.
Solution:
(b) 1210
The given series is 13, 17, 21....97.
$a_{1}=13, a_{2}=17, a_{n}=97$
$d=a_{2}-a_{1}=7-3=4$
$a_{n}=97$
$\Rightarrow a+(n-1) d=97$
$\Rightarrow 13+(n-1) 4=97$
$\Rightarrow n=22$
Sum of the above series:
$S_{22}=\frac{22}{2}\{2 \times 13+(22-1) 4\}$
$=11\{26+84\}$
$=1210$