For an A.P. show that `t _(m) + t _(2n + m) = 2 t _(m +n)`

For an A.P., show that (m +n)th term + (m-n) term =2 xx m th term

In an A.P., prove that : T_(m+n) + T_(m-n) = 2*T_(m)

If the sequence a_n is A.P., show that a_(m+n)+a_(m-n)=2a_mdot\

If S_n denotes the sum of first n terms of an A.P. such that (S_m)/(S_n)=(m^2)/(n^2),\ t h e n(a_m)/(a_n)= a. (2m+1)/(2n+1) b. (2m-1)/(2n-1) c. (m-1)/(n-1) d. (m+1)/(n+1)

The ratio of the sums of m and n terms of an A.P. is m^2: n^2 .Show that the ratio of m^(t h) and n^(t h) term is (2m" "-" "1)" ":" "(2n" "-" "1) .

If the m^(t h) term of an A.P. is 1/n and the n^(t h) terms is 1/m , show that the sum of m n terms is 1/2(m n+1)dot

If the m^(t h) term of an A.P. is 1/n a n d\ t h e\ n^(t h)t e r m\ i s1/m ,\ show that the sumof m n terms is 1/2(m n+1) where m!=ndot

Let {t_(n)} is an A.P If t_(1) = 20 , t_(p) = q , t_(q) = p , find the value of m such that sum of the first m terms of the A.P is zero .

If the sum of first m terms of an A.P is n and sum of first n terms of the same A.P is m, show that sum of first (m+n) terms of it is -(m+n) .

if m t h term of an A.P. is n\ a n d\ n t h term is m , then write its m+n t h term.