## Posts Tagged ‘geometric means’

## Problem 690

Write the geometric sequence that has four geometric means between 1 and 16,807.

**Solution:-**

an = a1 * r^{n -1}

Where an is the nth term, a1 is the first term and r is common ratio.

a1= 1 and a6 = 16807

16807 = 1*r^(6-1)

r = 7

geometric means between 1 and 16,807.

7,49,343,2401

## Problem 645

Find the three geometric means between and 8.

**Solution:-**

t1= , t5 = 8

t5 =

8=

8*2 =

16 =

r = 2

In geometric sequence we have to find the next number by multiply last number to common ratio.

*2 = 1

1*2 = 2

2 * 2 = 4

So the three geometric means 1, 2, 4

## Problem 644

Find the three geometric means between 2 and 162.

**Solution:-**

t1=2

t5=162

162 =

81 =

r = 3

In geometric sequence we have to find the next number by multiply last number to common ratio.

2*3 = 6

6*3 =18

18*3 = 54

So the three geometric means 6, 18, 54