Nth term of the series 1-4-5-7-52-10-53- will be A- 3 n-1-35 n-1B- 3 n5 n-1-35nC- 3 n5-2-5n-1 - 3n-2-5n-1

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Standard XII

Mathematics

Sigma n

nth term of t...

Question

$n^{t h}$ term of the series $1 + \frac{4}{5} + \frac{7}{5^{2}} + \frac{10}{5^{3}} + . . . . .$ will be

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Solution

The correct option is C
This series is clearly an A.G., the corresponding A.P. is $1 + 4 + 7 + 10 + . . . .$ having $n^{t h}$ term = 3n-2 and corresponding G.P. is $1 + \frac{1}{5} + \frac{1}{5^{2}} + . . . . .$ having $n^{t h}$ term = $\frac{1}{5^{n - 1}}$ Hence required $n^{t h}$ term of the series is $\frac{3 n - 2}{5^{n - 1}} .$

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nth term of the series 1+45+752+1053+..... will be

The correct option is C This series is clearly an A.G., the corresponding A.P. is 1+4+7+10+.... having nth term = 3n-2 and corresponding G.P. is 1+15+152+..... having nth term = 15n−1 Hence required nth term of the series is 3n−25n−1.

$n^{t h}$ term of the series $1 + \frac{4}{5} + \frac{7}{5^{2}} + \frac{10}{5^{3}} + . . . . .$ will be