Question

What is `a_9` for the geometric sequence `1/2, 1/4, 1/8, 1/16`?

Answer 1

The `"nth"` term of a geometric sequence is given by `t_n = a xx r^(n - 1)`

Explanation:

In this sequence, `a = 1/2`, `n = 9` and `r = ?`

The common ratio, abbreviated to `r`, can be found by using the formula `r = t_2/t_1`.

Calculating:

`r = t_2/t_1`

`r = (1/4)/(1/2)`

`r = 1/4 xx 2/1`

`r = 1/2`

Now, we know all the information we need to know to find `a_9`

`t_9 = 1/2 xx (1/2)^8`

`t_9 = 1/2 xx 1/256`

`t_9 = 1/512`

Therefore, the 9th term, or `a_9` is `1/512`.

Hopefully this helps!