Kamila Frye

Kamila Frye

Answered

2022-10-18

Find 3 geometric means between 3 and 1488

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Answer & Explanation

Audrey Russell

Audrey Russell

Expert

2022-10-19Added 16 answers

We are looking for 3 numbers a,b,c such that:
a is the geometric mean of 3 and b
b is the geometric mean of a and c
c is the geometric mean of b and 1488
That will make the following sequence into a geometric one:
3,a,b,c,1488
If the common ratio is r then we must have:
1488 = 3 r 4
So:
r 4 = 1488 3 = 496 = 2 4 31
in order that the geometric means be Real and positive, we need to choose the principal 4th root to find:
r = 2 31 4
Hence a,b,c are:
3 2 31 4 = 6 31 4
6 31 4 2 31 4 = 12 31
12 31 2 31 4 = 24 ( 31 4 ) 3

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