Question

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

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Answer 1

Given $t_n$ = 3.$2^n$.

Sum of the n terms

$S_n={\sum }_{i=1}^n{3.2}^n$

= 3 [$2^1+2^2+2^3+......nterms$]

Given series is a GP

Sum of n terms

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

For 10 terms substitute n = 10 in equation 1

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