[" (c) "512],[" If "b_(1),b_(2),b," are three consecutive terms of an arithmedic "],[" progression with common differenced,"30," then what "],[" is the value of "d" for which "b_(3)^(2)=b,b_(2)+b_(1)d+2?]

If b_(1),b_(2),b_(3) are three consecutive terms of an arithmetic progression with common difference dgt0, then what is the value of d for which b(2)/(3)=b_(2)b_(3)+b_(1)d+2?

Suppose 1/(a+b),1/(2b),1/(b+c) are three consecutive terms of an AP. Prove that a,b,c are the consecutive terms of a G.P.

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.

Suppose 1/(a+b),1/(2b),1/(b+c) are three consecutive terms of an AP. Prove that (a+b)(b+c)=b(a+2b+c)

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.

if b_(1),b_(2),b_(3)(b_(1)gt0) are three successive terms of a G.P. with common ratio r , the value of for which the inequality b_(3)gt4b_(2)-3b_(1) , holds is given by

Let a_(1), a_(2), a_(3)... be a sequance of positive integers in arithmetic progression with common difference 2. Also let b_(1),b_(2), b_(3)...... be a sequences of posotive intergers in geometric progression with commo ratio 2. If a_(1)=b_(1)=c_(2) . then the number of all possible values of c, for which the equality. 2(a_(1)+a_(2).+.....+a_(n))=b_(1)+b_(2)+....+b_(n) holes for same positive integer n, is

If a : b = c : d = 1 : 6, then what is the value of (a^2+c^2)/(b^2+d^2) ?