If a, b and c are three consecutive terms of an A.P.,prove that `k^a, k^b` and `k^c` are three consecutive terms of a G.P. Assume k to be a non-zero real number.

If 1/(x+y),1/(2y),1/(y+z) are three consecutive terms of an A.P., prove that x, y, z are three consecutive terms of a G.P.

Determine k so that k+2, 4k-6 and 3k-2 are three consecutive terms of an A.P.

Prove that a - 5b, a - b and a + 3b are consecutive term of an A.P.

Determine k so that : 2/3, k, 5/8 , are the three consecutive terms of an A.P.

Determine k so that : 8k + 4, 6k-2, 2k-7, are the three consecutive terms of an A.P.

If the mth, nth and pth terms of a G.P. form three consecutive terms of a geometric sequence, prove that m, n and p form three consecutive terms of an arithmetic sequence.

The sum of three Consecutive terms of an A.P. is 15 and sum of their Squares is 83. Find the terms.

The sum of three consecutive terms of an A.P. is 9 and the sum of their squares is 35. Find the terms.

If 9th term of an A.P. is zero, prove that its 29th term is double the 19th term.

The sum of three consecutive numbers of an A.P. is 27 and their product is 504. Find the numbers.