If are in A.P., prove that:

are in A.P.

There are n A.M.s between 3 and 17. The ratio of the last mean to the first mean is 3 : 1. Find the value of n.

If x, y, z are in A.P. and A₁is the A.M. of x and y, and A₂ is the A.M. of y and z, then prove that the A.M. of A₁ and A₂ is y.

Insert 7 A.M.s between 2 and 17.

The 10^th and 18^th term of an A.P. are 41 and 73 respectively, find 26^th term.

If 10 times the 10^th term of an A.P. is equal to 15 times the 15^th term, show that the 25^th term of the A.P. is Zero.

Insert five numbers between 8 and 26 such that the resulting sequence is an A.P

The 4^th term of an A.P. is three times the first and the 7^th term exceeds twice the third term by 1. Find the first term and the common difference.

In an A.P. the first term is 2, and the sum of the first 5 terms is one-fourth of the next 5 terms. Show that 20th term is - 112

Insert 4 A.M.s between 4 and 19.

Show that x² + xy + y², z² + zx + x² and y² + yz + z² are in consecutive terms of an A.P., if x, y and z are in A.P.