Question

Find the sum of all $2$- digit numbers divisible by $3$.

• A. $1335$
• B. $1445$
• C. $1665$
• D. $1555$

Answer 1

Answer: (C)

$1665$

Solution:- (C) 1665

First two digit number divisible by 3 = 12

Last two digit number divisible by 3 = 99

$\therefore$ First term, $\left(a\right)=12$

Common difference, $\left(d\right)=3$

Last term, $\left(l\right)=99$

$n=?$

As we know that,

$a_n=a+(n-1)d$

$\therefore 99=12+(n-1)3$

$\Rightarrow (n-1)\frac{87}{3}$

$\Rightarrow n=29+1=30$

$\therefore$ Sum of n terms of an A.P., when last term is known is given by-

$S_n=\frac{n}{2}(a+l)$

$\therefore S_{30}=\frac{30}{2}(12+99)$

$\Rightarrow S_{30}=15\times 111=1665$