How do you find nth term rule for 1/2,1/4,1/8,1/16,...?

Aug 21, 2016

${n}^{t h}$ term is $\frac{1}{2} ^ n$.

Explanation:

The series $\frac{1}{2} , \frac{1}{4} , \frac{1}{8} , \frac{1}{16} , \ldots .$ can be written as

$\frac{1}{2} ^ 1 , \frac{1}{2} ^ 2 , \frac{1}{2} ^ 3 , \frac{1}{2} ^ 4 , \ldots .$

Hence ${n}^{t h}$ term can be written as $\frac{1}{2} ^ n$.

Other way could be to treat it as a geometric series whose first term is ${a}_{1}$ and common ratio is $r$. The ${n}^{t h}$ term of the series is then given by a_1×r^(n-1).

As here ${a}_{1} = \frac{1}{2}$ and r=(1/4)/(1/2)=1/4×2/1=1/2, the ${n}^{t h}$ term is

1/2×(1/2)^(n-1) or

1/2×1/2^(n-1)=1/2^n.