What is the next number in the series 2, 1, 12 1 2 , 14 1 4 ...

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

Answer Details

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 × $\frac{1}{16}$
= $\frac{1}{8}$