In an A.P,if `a_m=1/n` and `a_n=1/m` then show that `a_(nm)=1`.

The sum of first n terms of an A.P. is S_n .If S_n=n^2p and S_m=m^2p(mnen) .Show that S_p=p^3 .

if m times the mth term of an A.P. is equal to n times the nth term and m!=n show that (m+n) th is zero.

If a_1, a_2, a_3 ….. a_n are in AP, then prove that frac(1)(a_1 a_2)+frac(1)(a_2 a_3)+frac(1)(a_3 a_4)+.....+frac(1)(a_(n-1) a_n)=frac(n-1)(a_1 a_n)

If the sum of first n,2n,3n terms of an A.P. be S_1 , S_2 and S_3 respectively then prove that S_1+S_3=2S_2

if tantheta+sintheta=m and tantheta-sintheta=n show that (m^2-n^2)^2=16mn

If the mth term and nth term of an A.P. are respectively n and m show that the (m + n)th term is zero and pth term is m + n-p .

If A and G be the A.M. and G.M. of two numbers a and b and A:G=m:n ,then prove that- a:b=m+sqrt(m^2-n^2) :m-sqrt(m^2-n^2)

In an AP:(viii) given a_n=4,d=2,S_n=-14 ,find n and a.

In an AP:(i) given a=5,d=3, a_n=50 ,find n and S_n

If the sum of first n,2n,3n terms of an A.P. be S_1 , S_2 and S_3 respectively then prove that S_3=3(S_2-S_1)