Question

Insert five geometric means between 1/8 and 8. There are supposed to be 2 answers

Answer 1

Answer:

Step-by-step explanation:

In a geometric sequence, the consecutive terms differ by a common ratio. The formula for determining the nth term of a geometric progression is expressed as

Tn = ar^(n - 1)

Where

a represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the information given,

a = 1/8

n = 7 terms

Since the last term is 8, then

8 = 1/8 × r^(7 - 1)

Multiplying through by 8, it becomes

64 = r^6

Taking the 6th root of both sides of the equation, then

r = 2

The 5 geometric means would be

1/8 × 2 = 1/4

1/4 × 2 = 1/2

1/2 × 2 = 1

1 × 2 = 2

2 × 2 = 4

The sequence is

1/8, 1/4, 1/2, 1, 2, 4, 8