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

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