Sequences and Series
the mean xˉ
Let the sum of n, 2n, 3n terms of an A.P. be S1,S2and S3, respectively, show that S3=3(S2−S1).
If S1,S2,S3are the sum of first n natural numbers, their squares and their cubes, respectively, show that 9S22=S3(1+8S1).
In an A.P., if pthterm is q1and qthterm is p1, prove that the sum of first pq terms is 21(pq+1),where p=q.