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

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

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Answer 1 · 2014-09-19T21:46:02

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: $7$ $7$

$7 \cdot 4 = 28$ $7 * 4 =28$

Second term: $28$ $28$

$28 \cdot 4 = 112$ $28 * 4=112$

Third term: $112$ $112$

$112 \cdot 4 = 448$ $112 * 4=448$

Fourth term: $448$ $448$

This geometric sequence can be further described by the equation:

$a_{n} = 7 \cdot 4^{n - 1}$ $a_n =7*4^(n-1)$

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

$a_{4} = 7 \cdot 4^{4 - 1} = 7 \cdot 4^{3} = 7 \cdot 64 = 448$ $a_4=7*4^(4-1)=7*4^(3)=7*64=448$

Note:

$a_{n} = a_{1} r^{n - 1}$ $a_n =a_1r^(n-1)$

where $a_{1}$ $a_1$ is the first term, $a_{n}$ $a_n$ is the actual value returned for a specific $n^{t h}$ $n^(th)$ term and $r$ $r$ is the common ratio.

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

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