Question

Find the common ratio of the sequence.

4, -4, 4, -4...

Answer 1

A geometric sequence is built with an initial value and a common ratio.

You start with the initial value
`x_0`, which is the first element of the sequence, and then you build the term
`x_i` by multiplying the previous element
`x_(i-1)` by the common ratio
`r`. So, the first terms of the sequence are

`x_0,\ x_1 = x_0\cdot r,\ x_2 = x_0\cdot r^2,\ x_3 = x_0\cdot r^3, \ldots`

In this sequence, every element is equal to the previous one, except the sign is opposite. This means that each element is computed by multiplying the previous one by
`-1`, which is thus the common ratio of the sequence.