The pth, qth and rth terms of an A.P. are a, b, c respectively. Show that (q – r) a + (r – p) b + (p – q)c = 0

Show that the sum of (m + n)^th and (m – n)^th terms of an A.P. is equal to twice the m^th term.

Find the sum to n terms of an A.P., whose nth term is

Solve the equation 1 + 6 + 11 + 16 + ........ + x = 148

How many terms of the A.P. -6, -5, .......... are needed to give the sum -25? Explain the double answer.

In a A.P., the first term is 2 and the sum of first five terms is one-fourth of the sum of the next five terms. Show that the 20th term is – 112.

If the sum of first n terms of a sequence is of the form An² + Bw, where A and B arc constants (independent of n). Show that the sequence is an A.P. Is the converse true? Justify your answer.

In an A.P., if the pth term is and the qth term is prove that the sum of the first pq terms must be where

If the pth term of an A.P. is a and qth term is b, show that the sum of (p + q) terms

is  

Find the sum of odd integers from 1 to 2001.