If m,n,s,t are in G.P , then 1/m,1/n,1/s,1/t , are in ?

1 Answer
Apr 29, 2018

Let the common ratio of the GP in Question be #r#.

Then, #n-:m=r, s-:n=r, t-:s=r............(ast)#.

Now, #1/n-:1/m=m/n=1/r............[because, (ast)]......(ast^1)#.

# 1/s-:1/n=n/s=1/r and 1/t-:1/s=s/t=1/r......(ast^2)#.

From #(ast^1) and (ast^2)#, we find,

#1/n-:1/m=1/s-:1/n=1/t-:1/s=1/r#.

This proves the assertion.