Suppose that a,b,c,d are in G.P with common ratio r Prove that `b+c=ar(1+r)` and `b+d=ar(1+r^2)`

Suppose that a,b,c,d are in G.P with common ratio r Prove that (b+c)(b+d)=(c+a)(c+d)

Suppose that a, b, c are in A.P. Prove that 2b = a + c

Suppose that a, b, c are in A.P. Prove that a^2(b+c),b^2(c+a),c^2(a+b) are in A.P.

If a,b,c are in G.P. with common ratio r_(1) and alpha , beta, gamma are in G.P. with common ratio r_(2) , and equations ax + alpha y + z = 0, bx + beta y + z = 0, cx + gamma y + z = 0 have only zero solution. Then which of the following is not true. a) r_(1)!=1 b) r_(2)!=1 c) r_(1)!=r_(2) d)None of these

Suppose a, b, c are in A.P.Prove that a(1/b+1/c),b(1/c+1/a),c(1/a+1/b) are in A.P.

Suppose a, b, c are in A.P. Prove that (a+2b-c)(2b+c-a)(c+a-b)=4abc

Suppose a^2,b^2,c^2 are in A.P. Prove that a/(b+c),b/(c+a),c/(a+b) are also in A.P.S

Suppose a^2,b^2,c^2 are in A.P. Prove that 2b^2=a^2+c^2

If a,b,c,d are in G.P. prove that (a^n+b^n),(b^n+c^n),(c^n+d^n) are in G.P.

If a, b, c, d are in G.P . Prove that (a^n+b^n),(b^n+c^n),(c^n+d^n) are in G.P .