Insert two numbers between 1 and -27 so that the resulting sequence is a G.P.

Insert two numbers between 3 and 24 so that the resulting sequence is a G.P.

Insert two numbers between -40 and -5, so that the resulting sequence is a G.P.

Insert two numbers between 1/4 and 1/3 so that the resulting sequence is a H.P.

Insert two numbers between (2)/(9) and (1)/(12) so that the resulting swquence is a HP.

Which 2 terms are inserted between 5 and 40 So that the resulting sequence is G.P.

Insert 4 terms between 2 and 22 so that the new sequence is in AP.

Which number should be subtracted from each of the numbers 13, 25 and 55 so that the resulting numbers would be in continued proportion?

If for a sequence, t_n = 2^(n - 1) / 5^(n - 1) , show that the sequence is a G.P. Find its first term and common ratio.