What is the next number in the series 2, 1, \(\frac{1}{2}\), \(\frac{1}{4}\)...

A.

\(\frac{1}{3}\)

B.

\(\frac{2}{8}\)

C.

\(\frac{3}{7}\)

D.

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

Correct answer is D

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

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

Tn = 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 × \(\frac{1}{16}\)

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