Question

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

Answer 1

`n^(th)` term is `1/2^n`.

Explanation:

The series `1/2,1/4,1/8,1/16,....` can be written as

`1/2^1,1/2^2,1/2^3,1/2^4,....`

Hence `n^(th)` term can be written as `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^(th)` term of the series is then given by `a_1×r^(n-1)`.

As here `a_1=1/2` and `r=(1/4)/(1/2)=1/4×2/1=1/2`, the `n^(th)` term is

`1/2×(1/2)^(n-1)` or

`1/2×1/2^(n-1)=1/2^n`.