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Question

If n arithmetic means are inserted between 20 and 80 such that the ratio of the first mean to the last mean is 1:3, then the value of n is

A
12
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B
6
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C
11
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D
5
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Solution

The correct option is C 11
Let A1,A2,,An be n A.M.s between 20 and 80.
Given, A1:An=1:3
3A1=An3[20+1(8020)n+1]=20+n(8020)n+160+180n+1=20+60nn+160(n3)n+1=4020n=220n=11

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