True or False :
A sequence obtained by multiplying the corresponding terms of two G.P.s is again a G.P.

We are given two G.P.'s, one with the first term 'a' and common ratio ‘r’ and the other with first term ‘b’ and common ratio ‘s’. Show that the sequence formed by the product of corresponding terms is a G.P. Find its first term and the common ratio. Show also that the sequence formed by the quotient of corresponding terms is G.P. Find its first term and common ratio.

Find the 20th and nth terms of the G.P. 5/2,5/4,5/8, .....

The sum of three numbers in G.P. is 42. If the first two numbers are increased by 2 and third is decreased by 4, the resulting numbers form A.P. Find the numbers of G.P.

The sum of three numbers which are consecutive terms of an A.P. is 21. If the second number is reduced by 1 and the third is increased by 1, we obtain three consecutive terms of a G.P. Find the numbers.

Find the n^(th) term of the G.P , 1/3 , 1/6 , 1/12 .....

The next term of the G.P. x ,x^2+2,a n dx^3+10 is

The sum of first ten terms of an A.P. is 155 and the sum of first two terms of a G.P. is 9. The first term of the A.P. is equal to the common ratio of the G.P., and the first term of the G.P. is equal to the common difference of the A.P. Find the two progressions.

If the mth, nth and pth terms of a G.P. form three consecutive terms of a geometric sequence, prove that m, n and p form three consecutive terms of an arithmetic sequence.

If the first and the nth term of a G.P. are a and b. respectively, and if P is the product of n terms, prove that P^2 = (ab)^n .

Find the 5^(th) term of the G.P , 1/2 , 1/4 ,1/8 ....