Question

Find the $n^{th}$ term of the series. 1 + 4 +13 +40 + 121 +.................

• A. (
• B. (
• C. (
• D. (

Answer 1

The correct option is B

(

$S_n$ = 1 + 4 + 13 + 40 + 121---------------(1)

$S_n$ = 1 + 4 + 13 + 40 +---------------(2)

Write the $S_n$ in such a way that $1^{st}$ term of equation 2 comes under $2^{nd}$ term of equation 1

Subtracting equation 2 term equation 1.

0 = 1 + 3 + $3^2$ + $3^3$ +----------------------($T_n$ - $T_{n-1}$) - $T_n$ ---------------(2)

$T_n$ = 1 + 3 + $3^2$ + $3^3$ +---------------------- n terms

$T_n$ = $\frac{1.(3^n-1)}{3-1}$ =$\frac{1}{2}$ ($3^n-1)$