Write the condition under which three numbers a,b,c may be in A.P and G.P both.

State the condtion under which P(A/B) = P(A).

Write the three condition of L. C . A . O.

x and y are two positive integers such that 2,x, y are in A.P. and x, y, 9 are in G.P. then show that -x= 4, y= 6.

The numbers x, 8, y (xney) are in G.P. and the numbers x, y,-8 are in A.P., then show that x = 16, y = 4

The product of three numbers in G.P. is 512. If 8 be added to the first, and 6 to the second, then these two sums and the third term form an A.P., find the numbers.

If the sum of three consecutive numbers of an A.P is 36 and the product of the three terms is 1140,find the term.

If a, b, c be the pth, qth and rth term of both an A.P. and G.P., then show that - a^(b-c).b^(c-a).c^(a-b)=1 .

Divide 69 into three parts such that the parts may form as A.P. and the product of first two terms is 483.

If a, b, c are in A.P. and also in GP., show that a = b = c.

The sum of three numbers in G.P. is 70. If the first and last term are multiplied by 4 and the middle term by 5, then they will be in A.P., find them.