Show that `(a - b), a` and `(a + b)` form consecutive terms of an A.P.

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

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 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.

The number of arrangements of the word " IDIOTS " such that vowels are at the places which form three consecutive terms of an A.P. is :

The number of arrangements of the word " IDIOTS " such that vowels are at the places which form three consecutive terms of an A.P. is :

If 1/(a+b),1/(2b),1/(b+c) are three consecutive terms of an A.P., prove that a ,b ,c are the three consecutive terms of a G.P.

Show that x^(2)+xy+y^(2),y^(2)+yz+z^(2), are consecutive terms of an A.P.if x,yandz are in A.P.

If a, b, c are three consecutive terms of an A.P. and x, y, z are three consecutive terms of a G.P. then prove that x^(b-c)timesy^(c-a)timesz^(a-b)=1

If a ,b ,c ,d are four consecutive terms of an increasing A.P., then the roots of the equation (x-a)(x-c)+2015(x-b)(x-d)=0 are

If second, third and sixth terms of an A.P. are consecutive terms of a G.P. write the common ratio of the G.P.