Question

If the sum of the first $40$ terms of the series, $3+4+8+9+13+14+18+19+\dots$ is $\left(102\right)m$, then $m$ is equal to :

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

Answer 1

The correct option is D $20$

$S=\underset{–}{3+4}+\underset{–}{8+9}+\underset{–}{13+14}+\underset{–}{18+19}+\dots \text{upto}40\text{terms}$

$\Rightarrow S=7+17+27+37+\dots \text{upto}20\text{terms}$
$\Rightarrow S=\frac{20}{2}[14+19\times 10]=20\times 102$

$\therefore m=20$