Sequence And Series Question 518
Question: $ n^{th} $ term of the series $ 1+\frac{4}{5}+\frac{7}{5^{2}}+\frac{10}{5^{3}}+…….. $ will be
Options:
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}}} $
Show Answer
Answer:
Correct Answer: C
Solution:
This series is clearly an A.G., the corresponding A.P. is $ 1+4+7+10+……… $ having $ n^{th} $ term $ =3n-2 $ and corresponding G.P. 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}}} $ . Trick: Check by putting $ n=1,\ 2 $ in alternates.
BETA
