Use the geometric mean to find the 7th term in a geometric sequence if the 6th term is 8 and the 8th term is 18?

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12
15
7
5

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Answer 1 · 2017-04-04T20:43:00

If the common ratio is positive, then the $7$ th term is $12$ .

If not, then it would be $-12$ .

In a geometric sequence of positive terms, the middle term of three consecutive terms is the geometric mean of the first and third.

Given two positive numbers $a$ and $b$ , their geometric mean is:

$sqrt(ab)$

In our example we find that the geometric mean of $8$ and $18$ is:

$sqrt(8*18) = sqrt(144) = 12$

So, assuming the common ratio of the geometric sequence is positive, the $7$ th term is $12$ .

Note that the $7$ th term could also be $-12$ , if the common ratio was $-3/2$ instead of $3/2$ .