Question

Find the three positive geometric means between 3 and 48/625

A. 9/5, 27/25, 81/125

B. 6/5, 12/25, 24/125

C. 3/5, 3/25, 3/125

D. 1, 1/3, 1/9

Answer 1

A

Explanation:

Answer 2

B. 6/5, 12/25, 24/125

Explanation:

Let the geometric means to be inserted be x, y and z. The geometric series will contain 5 terms as shown:

3, x, y, z, 48/625

Using the nth term of a geometric sequence to find the missing term.

`Tn = ar^(n-1)` where:

a is the first term

n is the number of terms and

r is the common ratio

From the sequence, a = 3

`T5 = 3r^(5-1) \\T5 = 3r^(4)`

Since the fifth term is 48/625 then:

`3r^(4)=(48)/(625) \\r^(4)= (48)/(625*3) \\r^(4) = (16)/(625) \\r=\sqrt[4]{(16)/(625) } \\r = (2)/(5)`

To get the 2nd, 3rd and 4th term, we will substitute the value of the first term and the common ratio in the equation given.

`T2 = 3((2)/(5) )^(2-1)\\ T2 = 3*2/5\\T2 = 6/5`

when n = 3;

`T3 = 3((2)/(5) )^(3-1)\\ T3 = 3*((2)/(5) )^(2) \\T3= 3*4/25\\T3 = 12/25`

when n = 4;

`T4 = 3((2)/(5) )^(4-1)\\ T4 = 3*((2)/(5) )^(3) \\T4= 3*8/125\\T4 = 24/125`

The three positive geometric mean are 6/5, 12/25, 24/125