Question

What is r, the common ratio, in the geometric sequence 2, −14, 98, −686

Answer 1

To find r, divide any number into the next number.
98/(-14) = -7

Answer 2

The common ratio r is -7.

Explanation:

The common ratio of a geometric sequence is the division of the term
`a_(n+1)` by the term
`a_(n)`.

In this problem, we have that:

`a_(1) = 2, a_(2) = -14, a_(3) = 98, a_(4) = -686`.

So the common ratio r is:

`r = (-14)/(2) = (98)/(-14) = (-686)/(98) = -7`

The common ratio r is -7.