Find the sum of 10 terms of the series whose $n^{t h}$ term is 3. $2^{n}$ .

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Solution

Given $t_{n}$ = 3. $2^{n}$ .

Sum of the n terms

$S_{n} = \sum_{i = 1}^{n} {3.2}^{n}$

= 3 [ $2^{1} + 2^{2} + 2^{3} + . . . . . . n t e r m s$ ]

Given series is a GP

Sum of n terms

$S_{n}$ = 3. $[\frac{2. (2^{n} - 1)}{(2 - 1)}]$ -------------(1)

For 10 terms substitute n = 10 in equation 1

$S_{10}$ = 3. $[\frac{2. (2^{10} - 1)}{(2 - 1)}]$ = 3.[2 $\times$ (1023)] = 6144

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