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

Sep 19, 2014

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: $7$

$7 \cdot 4 = 28$

Second term: $28$

$28 \cdot 4 = 112$

Third term: $112$

$112 \cdot 4 = 448$

Fourth term: $448$

This geometric sequence can be further described by the equation:

${a}_{n} = 7 \cdot {4}^{n - 1}$

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

${a}_{4} = 7 \cdot {4}^{4 - 1} = 7 \cdot {4}^{3} = 7 \cdot 64 = 448$

Note:

${a}_{n} = {a}_{1} {r}^{n - 1}$

where ${a}_{1}$ is the first term, ${a}_{n}$ is the actual value returned for a specific ${n}^{t h}$ term and $r$ is the common ratio.