Question

The nth term of a series is given to be $\frac{3+n}{4}$, find the sum of $105$ terms of this series.

Answer 1

Putting $n=1,2,3,$______ in $T_n=(3+n)/4$
We get the series as $1,\frac{5}{4},\frac{3}{2},$_______
$\therefore a=1,d=\frac{1}{4}$.
$S_{105}=\frac{105}{2}[2.1+(104\left)\frac{1}{4}\right]$
$=\left(105/2\right)\times 28=1470$.