For a sequence $\left(t_{n}\right)$ if $s_{n}=7\left(3^{n}-1\right)$, then $t_{n}=$
For a sequence $\left(t_{n}\right)$ if $s_{n}=7\left(3^{n}-1\right)$, then $t_{n}=$
- $(7) 3^{n-1}$
- (14) $3^{n+1}$
- $(14) 3^{n-1}$
- $\quad(7) 3^{n+1}$
Solution
A sequence; $t_{n} ;$
$\begin{aligned}
s_{n} &=7\left(3^{n-1}\right) \\
s_{n-1} &=7\left(3^{n-1}-1\right) \\
&
\end{aligned}$
$\begin{aligned}
t_{n} &=s_{n}-s_{n-1} \\
t_{n} &=7\left(3^{n}-3^{n-1}\right) \\
&=7 \cdot 3^{n-1} \cdot 2 \\
&=14 \cdot 3^{n-1}
\end{aligned}$
Asked in: MHT CET 2020 (14 Oct Shift 1)
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