Question

Given that the third term `a_3` of a geometric sequence is `2` and the sixth term `a_6` is `128`, which term is `1/2` ?

Answer 1

`a_2`

Explanation:

We can write the general term of a geometric sequence as:

`a_n = ar^(n-1)`

where `a` is the initial term and `r` is the common ratio.

In our example `a_3 = ar^2` and `a_6=ar^5` so we find:

`r^3 = (ar^5)/(ar^2) = a_6/a_3 = 128/2 = 64 = 4^3`

So the only possible Real value of `r` is `root(3)(4^3) = 4`

Note that `1/2 = 2/4 = a_3/r`.

So `a_2 = 1/2`