Sequences and Series
If x, y, z are in A.P. and tan−1x,tan−1yandtan−1zare also in A.P., then
Let the sum of n, 2n, 3n terms of an A.P. be S1,S2and S3, respectively, show that S3=3(S2−S1).
The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
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.