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The third mean of a GP of two numbers 27 and 1/27 is 1. Find the number of means. ​

Sagot :

DXGamer

Answer:

The mean is [tex]\sqrt{3}.[/tex]

Step-by-step explanation:

reinhard10158

Step-by-step explanation:

how unusual to call this that way.

I think you (and your teacher) mean the third term in a geometric sequence (or geometric progression, hence GP) between 27 and 1/27 is 1.

that means the sequence goes

27, a2, a3, 1, ..., 1/27

and so, "the number of means" is the number of terms between 27 and 1/27.

I happen to know that 27 is 3³. and that fits perfectly.

a2 = a1/3 = 27/3 = 9

a3 = a2/3 = 9/3 = 3

a4 = q = a3/3 = 3/3 = 1

correct. so, the common ratio is 1/3 (every new term of the sequence is created by multiplying the previous term by 1/3).

and then, if we continue, we get

a5 = a4/3 = 1/3

a6 = a5/3 = 1/3 / 3 = 1/9

a7 = a6/3 = 1/9 / 3 = 1/27

so the terms between 27 and 1/27 are a2, a3, a4, a5 and a6. that are 5 terms "in between" or 5 "means" between 27 and 1/27.

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