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?

12
15
7
5

Answer 1

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#.
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Answer 2

To find the 7th term in a geometric sequence, we can use the geometric mean. Given that the 6th term is 8 and the 8th term is 18, we can find the common ratio ((r)) of the sequence by dividing the 8th term by the 6th term. Then, we can use the geometric mean formula to find the 7th term.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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