Question

Identify the type of the following sequence:
$3+\frac{1}{4}(3+p)+\frac{1}{4^2}(3+2p)+\frac{1}{4^3}(3+3p)+.......$

• A. AP
• B. GP
• C. AGP
• D. HP

Answer 1

The correct option is C AGP

Here, in the series:

$3,(3+p),(3+2p),(3+3p),.....$ are in A.P. with common difference $p$

and $1,\frac{1}{4},\frac{1}{4^2},\frac{1}{4^3}$ are in G.P.

$\therefore$ The series is in A.G.P.

Hence, the answer is AGP.