Question

If the sum of the first $40$ term of the series $3+4+8+9+13+14+18+19+\cdots$ is $102\left(m\right)$, then the value of $m$ is

• A. $25$
• B. $20$
• C. $10$
• D. $5$

Answer 1

The correct option is B $20$

Let $S=(3+4)+(8+9)+(13+14)+(18+19)+\cdots$
$\Rightarrow S=7+17+27+37+\cdots \text{upto}20\text{terms}$
The terms of $S$ are in A.P.
Here $a=7,d=10,n=20$
$\therefore S=\frac{20}{2}\left[\right(2\times 7)+(19\times 10\left)\right](\because S_n=\frac{n}{2}[(2a+(n-1\left)d\right)\left]\right)$
$=\frac{20}{2}\times 204$
$=20\times 102$
$\therefore m=20$