How do you find the 7th term in the geometric sequence 2, 6, 18, 54, ...?

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How do you find the 7th term in the geometric sequence 2, 6, 18, 54, ...?

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Answer 1 · 2015-11-10T11:05:53

$4374$

Explanation:

In a geometric sequence, you choose a first term $a$ , a ratio $r$ , and then you obtain every term multiplying the previous one by the ratio. Let's compute some terms:

$a_0 = a$
$a_1 = a*r$
$a_2 = (a*r)r = a*r^2$
$a_3 = (a*r^2)r = a*r^3$

and so on. We can see that the relation is $a_n = a*r^n$ , which means that the seventh term is $a_7=a*r^7$ .

In your case, the first term $a$ is $2$ , and the ratio can be easily computed: if $a_0=2$ and $a_1=6$ , then $a_1=a_0*r=6$ , which means $2*r=6$ , and finally $r=3$ .

So, the seventh term will be $2*3^7 = 2*2187 = 4374$

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How do you find the 7th term in the geometric sequence 2, 6, 18, 54, ...?

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