If `t_(k)` is the `k^(th)` term of a G.P, then show that `t_(n-k),t_(n),t_(n+k)` also form a GP for any positive integer k.

If t_(n)" is the " n^(th) term of an A.P., then t_(2n) - t_(n) is …..

If t_(n)" is the " n^(th) term of an A.P. then the value of t_(n+1) -t_(n-1) is ……

Let T , be the r^(th) term of an A.P. whose first term is a and common difference is d If for some positive integers m, n, m != n , T_(m) = 1/n and T_(n) = 1/m , then a - d equals

If A=[(3,-4),(1,-1)] prove that A^k=[(1+2k,-4k),(k,1-2k)] where k is any positive integer.

If the nth term of an A.P. is t_(n) =3 -5n , then the sum of the first n terms is ………

Let t_(n) denote the n^(th) term in a binomial expansion. If t_(6)/t_(5) in the expansion of (a + b)^(n + 4) and t_(5)/t_(4) in the expansion of (a + b)^(n) are equal, then n is

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 .

Assertion: 1+2 + 3 + ... n = (n(n+1))/2 Reason: In a statement P(n), if P(l) is true and assuming P(k) and if we prove P(k + 1) is also true then P(n) is true for all value n, n is true integer

If p ,q ,a n dr are inA.P., show that the pth, qth, and rth terms of any G.P. are in G.P.