Question

Find the sum of all numbers from $50$ to $350$ which are divisible by $6$. Hence find the ${15}^{th}$ term of that A.P.

Answer 1

The numbers from $50$ to $350$ which are divisible by $6$ are $54,60,66,.....,348$.
The sequence is in A.P. in which $a=54,t_n=348=l$ and $d=6$.
We have, $t_n=a+(n-1)d$
$348=54+(n-1)6$
$348=54+6n-6$
$300=6n$
$\therefore n=50$
Now, $S_n=\frac{n}{2}[a+t_n]$
$S_{50}=\frac{50}{2}(54+348)$
$S_{50}=\frac{50}{2}\times 402$
$S_{50}=10.050$
Now, $t_{15}=54+(15-1)6$
$t_{15}=54+84$
$\therefore t_{15}=138$