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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7
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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#.