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

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

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Solution: Let A_1,A_2,...........A_n be n Arithmetic means between 20 and 80 and letd be the common diffrence

\d=(80-20)/n+1=60/n+1\ \Rightarrow [ecause d=(b-a)/n+1]\ \Rightarrow A_1=20+d=20+60/n+1=20(n+4/n+1)\ \Rightarrow A_n=20+nd=20+60n/n+1=20(4n+1/n+1)\ \ herefore A_1/A_n=n+4/4n+1=1/3Rightarrow n=11

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Deependra Verma

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