If the first and the nth terms of a GP are a and b respectively and if P is the product of the first n terms, then `P^(2)` is equal to

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 .

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

If the 5th and 12th terms of an A.P. are 30 and 65 respectively, what is the sum of the first 20 terms ?

5th term of a G.P. is 2, then the product of first 9 terms is:

The third term of a GP is 3. What is the product of the first five terms?

The fourth, seventh, and the last term of a G.P. are 10, 80, and 2560, respectively. Find the first term and the number of terms in G.P.

The first and last terms of an A.P. are a and l respectively. Show that the sum of nth term from the beginning and nth term from the end is a + l.

How many terms are there in A.P. whose first and fifth terms are -14 and 2 respectively and the sum of terms is 40 ?

The sum of the third and the seventh term of an A.P. is 6 and their product is 8. Find the sum of first sixteen terms of an A.P.

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.