A) \[\frac{3n+1}{{{5}^{n-1}}}\]
B) \[\frac{3n-1}{{{5}^{n}}}\]
C) \[\frac{3n-2}{{{5}^{n-1}}}\]
D) \[\frac{3n+2}{{{5}^{n-1}}}\]
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.
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