Question

Question #943a8

Answer 1

`u_(7) = 729`

Explanation:

We have: `1, - 3, 9, - 27, ...`

This geometric sequence has a common ratio of `- 3`.

The `n`th term of any geometric sequence is `u_(n) = u_(1) r^(n - 1)`; where `u_(1)` is the first term, `r` is the common ratio, and `n` is the number of the term.

We need to find the seventh term, i.e. `u_(7)`.

Let's plug in the relevant values into the `n`th term formula:

`Rightarrow u_(7) = 1 cdot (- 3)^(7 - 1)`

`Rightarrow u_(7) = (- 3)^(6)`

`therefore u_(7) = 729`

Therefore, the seventh term of the geometric sequence is `729`.