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

If a_(m) be the mth term of an AP, show that a_(1)^(2)-a_(2)^(2)+a_(3)^(2)-a_(4)^(2)+"...."+a_(2n-1)^(2)-a_(2n)^(2)=(n)/((2n-1))(a_(1)^(2)-a_(2n)^(2)) .

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^(th) and n^(th) term is (2m-1) : (2n -1) .

The numbers 1,3,6,10,15,21,28."……" are called triangular numbers. Let t_(n) denotes the bth triangular number such that t_(n)=t_(n-1)+n,AA n ge 2 . If (m+1) is the nth triangular number, then (n-m) is

The ratio of the sum of ma n dn terms of an A.P. is m^2: n^2dot Show that the ratio of the mth and nth terms is (2m-1):(2n-1)dot

For as Ap. S_(n)= m and S_(m) = n . Prove that S_(m+n)=-(m+n).(m ne n)

The numbers 1,3,6,10,15,21,28."……" are called triangular numbers. Let t_(n) denotes the n^(th) triangular number such that t_(n)=t_(n-1)+n,AA n ge 2 . The number of positive integers lying between t_(100) and t_(101) are

The numbers 1,3,6,10,15,21,28."……" are called triangular numbers. Let t_(n) denotes the bth triangular number such that t_(n)=t_(n-1)+n,AA n ge 2 . The value of t_(50) is

In an A.P. if m^("th") term is n and the n^("th") term is m, where m ne n , find the pth term .

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

Show that the sequence t_(n) defined by t_(n)=2*3^(n)+1 is not a GP.