If a, b, c are in A.P. then show that `3^(a), 3^(b), 3^(c)` are in G.P.

If a,b,c are in A.P., show that (a-c)^(2)=4(b^(2)-ac) .

Statement 1: The number of ways in which three distinct numbers can be selected from the set {3^1,3^2,3^3, ,3^(100),3^(101)} so that they form a G.P. is 2500. Statement 2: if a ,b ,c are in A.P., then 3^a ,3^b ,3^c are in G.P.

If the angles A,B,C of a triangle are in A.P. and sides a,b,c, are in G.P., then prove that a^2, b^2,c^2 are in A.P.

Suppose a, b, c are in a.P and a^(2), b^(2), c^(2) are in G.P. If a lt b lt c and a + b + c = 3/2 then the value of a Is

If a(1/b + 1/c), b(1/c + 1/a), c(1/a + 1/b) are in A.P., prove that a, b, c, are in A.P.

If a , b ,a n dc are in G.P., then a+b ,2b ,a n db+c are in a. A.P b. G.P. c. H.P. d. none of these

If a ,b ,c are in A.P., then prove that the following are also in A.P. a^2(b+c),b^2(c+a),c^2(a+b)

If a ,b ,c are in A.P., then prove that the following are also in A.P. a(1/b+1/c),b(1/c+1/a),c(1/a+1/b)

If a ,b ,c are in A.P., then prove that the following are also in A.P. 1/(sqrt(b)+sqrt(c)),1/(sqrt(c)+sqrt(a)),1/(sqrt(a)+sqrt(b))

If (b-c)^2,(c-a)^2,(a-b)^2 are in A.P., then prove that 1/(b-c),1/(c-a),1/(a-b) are also in A.P.