Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that `P^(2)R^(n) = S^n` .

Let S be the sum, P be the product and R be the sum of the reciprocals of 3 terms of G.P. Then P^(2) R^(3) : S^(3) is equal to :

Let a,b,c are respectively the sums of the first n terms, the next n terms and the next n terms of a GP. Show that a,b,c are in GP.

If the first and the n^("th") 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 .

Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from (n + 1)^("th") " to " (2n)^("th") term is 1/r^n .

If the sum of first term of an A.P is 49 and that of 17 terms is 289. Find the sum of first "n" terms. OR The sum of the third and seyenth terms of an AP is 6 and their product is 8. find the sum of first sixteen terms of the A.P.

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

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

Let S_(n) denote the sum of first n terms of an A.P. If S_(2n) = 3S_(n) , then the ratio ( S_(3n))/( S_(n)) is equal to :

If the sum of m terms of an A.P. is equal to the sum of either the next n terms or the next p terms, then prove that (m+n)(1/m-1/p)=(m+p)(1/m-1/n)dot