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: 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
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 × \(\frac{1}{16}\)
= \(\frac{1}{8}\)
