Correct Answer: Option D

Explanation

2, 1, \(\frac{1}{2}\), \(\frac{1}{4}\).....

There are 4 terms in the series
Therefore the next number will be the 5th term

T_n = ar\(^{n − 1}\) (formular for geometric series)

a = first term = 2

r = common rate = \(\frac{\text{next term}}{\text{previous term}}\) = \(\frac{1}{2}\)

n = number of terms

T₅ = 5th term = ?

T₅ = ar\(^{5 - 1}\)

= ar\(^4\)

= 2 × (ar\(^{n − 1}\))⁴

= 2 × \(\frac{1}{16}\)

= \(\frac{1}{8}\)

There is an explanation video available below.

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