Q. $n$th term of the series $1 + \frac{4}{5} + \frac{7}{5^{2}} + \frac{10}{5^{3}} + ...$ will be
A) $\frac{3n + 1}{5^{n - 1}}$
B) $\frac{3n - 1}{5^{n}}$
C) $\frac{3n - 2}{5^{n - 1}}$
D) $\frac{3n + 2}{5^{n - 1}}$
Explanation
(c)
The given series is clearly an AG, the corresponding AP is $1 + 4 + 7 + 10 + ...$ having $n$th term $= 3n - 2.$
and corresponding GP is $1 + \frac{1}{5} + \frac{1}{5^{2}} + ...\$having $n$th term $= \frac{1}{5^{n - 1}}$
Hence, required $n$th term of the series is $\frac{3n - 2}{5^{n - 1}}$.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.