Question

there are n arithmetic means between 3 and 27 of an AP . The ratio of the last mean to first mean is 5:1 . Find the value of n

Answer 1

For the Series A1,A2,...An, with common difference d,

given that AM:  b=27 and a=3

d = (b-a)/n+1 = (27-3)/(n+1) = 24/(n+1)

A1=a+d = 3 + (24/n+1) = (3n+27)/(n+1)

IIIly, An = 3+(24*n/(n+1)) = (27n+3)/(n+1)

Now, Given that A1:An = 5:1

therfore, An / A1 = (27n+3) / (3n+27)  = 5/1

or, 27n+3 = 5(3n +27)

solving for n,

27n+3=15n+135

12n=132

n=11, hence the answer.

Answer 2

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