Q94 / 150 · MHT CET 2019 (Shift 1) · Mathematics

For a sequence $(t_{n})$ , if $S_{n} = 5 (2^{n} - 1)$ then $t_{n} = \dots$

A
$5 (2^{n + 1})$
B
$\frac{5 \times 2^{n}}{4}$
Correct answer
C
$5 (2^{n - 1})$
D
$\frac{2 \times (2^{n - 1})}{5}$

Solution

We have,

S_{n} = 5 (2^{n} - 1)

We know that

a_{n} = S_{n} - S_{n - 1}

= 5 (2^{n} - 1) - 5 (2^{n - 1} - 1)

= 5 (2^{n} - 2^{n - 1})

= 5 (2^{n - 1})

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

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