" 14.For an A.P.show that "t_(m)+t_(2n+m)=2t_(m+n)

For an A.P.show that t_(m+n)+t_(m-n)=2t_(m)

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

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

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

Let t_(r) denote the r^(th) term of an A.P.Also suppose t_(m)=(1)/(n) and t_(n)=(1)/(m) for some positive integers m and n then which of the following is necessarily a root of the equation? (l+m-2n)x^(2)+(m+n-2l)x+(n+l-2m)=0

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

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

Let S_(n) and Delta_(n) be the sum of first n terms of 2 A. P' s whose rth term are T_(r) and t_(r) respectively.If (S_(n))/(Delta_(n))=(2n+5)/(3n+2) then (T_(11))/(t_(11))=(m_(1))/(m_(2)) where m_(1) and m_(2) are coprime. Find the value of (m_(2)-m_(1))/(2)=

If in an HP, t_m=n and t_n=m then prove that t_(m+n)=(mn)/(m+n) .

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) .