Question

Find an explicit formula for the geometric sequence −25,−50,−100,−200

Answer 1

`a_n = -25 \cdot 2^(n-1),\ \forall \, n \geq 1`

The general formula for a geometric sequence is:


`a_n = a_1 \cdot r^(n-1),\ \forall \, n \geq 1`

where
`a_1` is the first term, and
`r` is the ratio.

You can guess the ratio by dividing any term by the previous one. In this case, for example, -50/-25 = 2, and the ratio is 2.