Question

For the following geometric sequence find the explicit formula.
(12, -6, 3, ...]

Answer 1

Answer:
`a_n=12(-(1)/(2))^(n-1)`

Explanation:

Let's first find the common ratio this sequence. To get to the next term, we divide by 2 and we alternate signs. Hence, the common ratio is
`-(1)/(2)`.

We can now use the formula
`a_n=a_1(r)^(n-1)` to get the formula, where
`a_1` is the first term and r is the common ratio.

`a_n=a_1(r)^(n-1)\\a_n=12(-(1)/(2))^(n-1)`