Question

Find the nth term of the following series $2+5x+8x^2+11x^3+......$

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Given series is $2+5x+8x^2+11x^3+.......$ --------(1)
We see that
2,5,8,11.......... is an A.P

$n^{th}$ term is of $AP=2+(n-1)\times 3=2+3n-3=3n-1$
we also see that
$1,x,x^2,x^3......$ is a G.P
$n^{th}$ term of GP = $1.(x{)}^{n-1}=x^{n-1}$
Equation 1 is combination of AP and GP which is also called an AGP
$n^{th}$ term of the series of AGP=$n^{th}$ term of $AP\times n^{th}$ term of GP
$=(3n-1)\times x^{n-1}$
$n^{th}$ term of the series $=(3n-1)x^{(n-1)}$