The nth term of the series 5-7-13-31-85- is

The correct option is C 4+ 3 ^ n 1 Let S _ n =5+7+13+31+85+⋯ + T _ n 1 + T _ n #160; #160; #160; #160; #160; #160; 0=5+[ 2+6+18 ...

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Standard XII

Mathematics

General Term of Binomial Expansion

The nth ter...

Question

The $n$ th term of the series $5 + 7 + 13 + 31 + 85 + \dots$ is

3^{n - 1} + 2

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3 + 3^{n - 1}

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4 + 3^{n - 1}

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None of these

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Solution

The correct option is C $4 + 3^{n - 1}$
Let $S_{n} = 5 + 7 + 13 + 31 + 85 + \dots + T_{n - 1} + T_{n}$
$0 = 5 + [2 + 6 + 18 + \dots t o (n - 1) t e r m s] - T_{n}$
$\Rightarrow T_{n} = 5 + [2 + 6 + 18 + \dots t o (n + 1) t e r m s]$
$= 5 + \frac{2 (3^{n - 1} - 1)}{3 - 1}$ $[∵ S_{n} = \frac{a (r^{n} - 1)}{r - 1}, r > 1]$
$= 5 + 3^{n - 1} - 1 = 4 + 3^{n - 1}$

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The nth term of the series 5+7+13+31+85+⋯ is

The correct option is C 4+3n−1Let Sn=5+7+13+31+85+⋯+Tn−1+Tn 0=5+[2+6+18+⋯to(n−1)terms]−Tn⇒Tn=5+[2+6+18+⋯to(n+1)terms] =5+2(3n−1−1)3−1 [∵Sn=a(rn−1)r−1,r>1] =5+3n−1−1=4+3n−1

The $n$ th term of the series $5 + 7 + 13 + 31 + 85 + \dots$ is