Question

For the following geometric sequence, find the recursive formula and the 5th term in the sequence. In your final answer, include all of your work.

{-4, 12, -36, ...}

Answer 1

...42, -193.. thats the 4th and 5th

Answer 2

`a_n = (-3) *a_(n-1) \\ a_5 = -324`

Explanation:

Let's remember the definition of geometric sequence:

Each term is found by multiplying the previous term by a constant.

We need to find out that constant. As it's always the same, we just need to divide the second term by the first one to get it.

`12/-4 = -3`

The recursive formula will be:

`a_1 = -4 \\ a_n = (-3) *a_(n-1)`

With this, to find the 5th term in the sequence we need the fourth one first

`a_4 = (-3) *a_3 = (-3) *(-36) = 108\\ a_5 = (-3) *a_4 = (-3) *108 = -324`

`a_5 = -324`