Question

Sum of $n$ terms of the series $5+7+13+31+85+...,$ is

• A. $4n+\frac{1}{2}(3^n-1)$
• B. $8n+\frac{1}{2}(3^n-1)$
• C. $2n+\frac{1}{2}(3^n-1)$
• D. None of these

Answer 1

Answer: (A)

$4n+\frac{1}{2}(3^n-1)$

The given series is $5+7+13+31+85+.............$

$\Rightarrow 4n+(1+3+9+27+81+..........)$

$\Rightarrow 4n+(1+3+3^2+3^3+3^4+...........)$

$\Rightarrow 4n+\frac{1}{2}(3^n-1)$

Therefore option $A$ is correct