The 6th term is 8 and the 8th term is 18, use the geometric mean to find the 7th term in a geometric sequence

shiya43

shiya43

Answered question

2022-10-18

The 6th term is 8 and the 8th term is 18, use the geometric mean to find the 7th term in a geometric sequence

Answer & Explanation

Kyle Delacruz

Kyle Delacruz

Beginner2022-10-19Added 21 answers

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:
a b
In our example we find that the geometric mean of 8 and 18 is:
8 18 = 144 = 12
So, assuming the common ratio of the geometric sequence is positive, the 7th term is 12.
Note that the 7th term could also be −12, if the common ratio was - 3 2 instead of 3 2 .

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