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 $t_{n}=$
  1. $(7) 3^{n-1}$
  2. (14) $3^{n+1}$
  3. $(14) 3^{n-1}$
  4. $\quad(7) 3^{n+1}$

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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