Question

insert 3 geometric mean between 16 and 256

Answer 1

Let the geometric means be a1, a2 and a3
Then 16, a1, a2, a3, 256 form GP
First term is 16 and 5th term is 256
Let r be the common ratio
$16 \times {r}^{5 - 1} = 256 \\ {r}^{4} = \frac{256}{16} = 16 = {2}^{4} \\so \: \: r = 2 \\ \\ a1 = 16 \times 2 = 32 \\ a2 = a1 \times 2 = 64 \\ a3 = a2 \times 2 = 128$

Answer 2

32 , 64 & 128 are  3 geometric mean between 16 and 256

Step-by-step explanation:

3 geometric mean between 16 and 256

√ (16 * 256)

= √ 16 * 16 * 16

= 16 * 4

= 64

Between 16 & 64   & 64 & 256

= √(16 * 64)

= 32

√(64 * 256)

= 64 * 2

= 128

Hence three geometric means between 16 & 256

32 , 64 & 128

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