Question

What is the common ratio of the geometric sequence 7, 28, 112,...?

Answer 1

The common ratio for this problem is 4.

The common ratio is a factor that when multiplied by the current term results in the next term.

First term: `7`

`7 * 4 =28`

Second term: `28`

`28 * 4=112`

Third term: `112`

`112 * 4=448`

Fourth term: `448`

This geometric sequence can be further described by the equation:

`a_n =7*4^(n-1)`

So if you want to find the 4th term , `n=4`

`a_4=7*4^(4-1)=7*4^(3)=7*64=448`

Note:

`a_n =a_1r^(n-1)`

where `a_1` is the first term, `a_n` is the actual value returned for a specific `n^(th)` term and `r` is the common ratio.