# Find the common ratio of the geometric sequence 7, 28, 112,...

Find the common ratio of the geometric sequence 7, 28, 112,...
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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 nth term and r is the common ratio.