If S_n=4 (3^n-1 ), find T_ n+1 - Vidyadip

Question

If $S_n=4\left(3^n-1\right)$, find $T_{n+1}$

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Answer

$S_n=4\left(3^n-1\right.$
Now, $T _{ n +1}= S _{ n +1}- S _{ n }$
$=4\left[3^{n+1}-1\right]-4\left[3^n-1\right]$
$\left.=4\left[3^{n+1}-1\right]-3^n+1\right]$
$=4\left[3^n(3-1)\right]$
$=4\left(3^n \times 2\right)$
$\therefore T_{n+1}=8\left(3^n\right)$

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