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Question

Three geometric means between 5 and 3125 are___.

A
15,75,375
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B
25,125,625
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C
11,44,176
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D
10,40,160
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Solution

The correct option is B 25,125,625

The geometric mean is a geometric series which is in the form of arn where a is the first term and r is the common ratio.

T1= 5 and T5 = 3125

Now, T1/T5 = 5/ 3125

=>ar1//ar5 =1/ 625

=> 1/ r4 = 1/625

=> r4 = 625

=> r = 5

So if r=5, then a= 1

T2 = ar2

= 1(5) 2 = 25

T3 = ar3

= 1(5) 3 = 125

T4 = ar4

= 1(5)4 = 625

Therefore, three geometric means between 5 and 3125 are 25, 125 and 625.


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