First slide

Arithmetico-Geometric Progression

Question

nth term of the series $1 + \frac{4}{5} + \frac{7}{5^{2}} + \frac{10}{5^{3}} + \dots$ will be

Easy

A

$\frac{3 n + 1}{5^{n - 1}}$
B

$\frac{3 n - 1}{5^{n}}$
C

$\frac{3 n - 2}{5^{n - 1}}$
D

$\frac{3 n + 2}{5^{n - 1}}$

Solution

The given series is clearly an AG, the corresponding AP is $1 + 4 + 7 + 10 + \dots$ having nth term = $3 n - 2$ .
and corresponding GP is $1 + \frac{1}{5} + \frac{1}{5^{2}} + \dots$ having nth term $= \frac{1}{5^{n - 1}}$
Hence, required nth term of the series is $\frac{3 n - 2}{5^{n - 1}}$ .

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