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\frac{1}{2} and 8.

 

Solution:-

 

 

t1=\frac{1}{2} , t5 = 8
 
t5 = r^{(n-1)}
 
8= \frac{1}{2}* r^{5-1}
 
8*2 = r^{4}
 
16 = r^{4}
 
r = 2
 
In geometric sequence we have to find the next number by multiply last number to common ratio.
\frac{1}{2} *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 =2* r^{5-1}
81 = r^{4}
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