Q58 / 150 · MHT CET 2020 (13 Oct Shift 1) · Mathematics

For a sequence if $S_{n}=\frac{5^{n}-2^{n}}{2^{n}}$, then its fourth term is

  • Correct answer
    A
    $\frac{375}{16}$
  • B
    $\frac{375}{8}$
  • C
    $\frac{251}{8}$
  • D
    $\frac{251}{16}$

Solution

$s_{n}=\frac{5^{n}-2^{n}}{2^{n}} ; s_{n-1}=\frac{5^{n-1}-2^{n-1}}{2^{n-1}}$ $\begin{aligned} T_{n} &=s_{n}-s_{n-1} \\ T_{n} &=\frac{5^{n}-2^{n} \cdot 5^{n-1}}{2^{n}} \\ T_{4} &=\frac{5^{4}-2 \cdot 5^{3}}{2^{4}} \\ &=\frac{625-250}{16} \\ &=\frac{375}{16} \end{aligned}$

Hence, the correct answer is option: 'A'.

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