If a, b, c are in geometric progression, and if `a^(1/x)=b^(1/y)=c^(1/z)`, then prove that x, y, z are in arithmetic progression.

If a,b,c are in geometric progression, and if a^(1/x) = b^(1/y) =c^(1/z) , then prove that x,y,z arithmetic progression.

If a,b,c are in G.P and a^(1/x) = b^(1/y) = c^(1/z) , prove that x,y,z are in A.P.

If the roots of (a-b)x^(2)+(b-c)x+(c-a)=0 are real and equal, then prove that b, a, c are in arithmetic progression.

The first term of an arithmetic progression is 1 and the sum of the first nine terms equal to 369 . The first and the ninth term of a geometric progression coincide with the first and the ninth term of the arithmetic progression. Find the seventh term of the geometric progression.

If y^2=x z and a^x=b^y=c^z , then prove that (log)_ab=(log)_bc

If x,y,z are in G.P and a^x=b^y=c^z ,then

If a^x=b ,b^y=c ,c^z=a , then find the value of x y zdot

Write the first 6 terms of the sequences whose n^(th) terms are given below and classify them as arithmetic progression, geometric progression, arithmetico-geometric progression, harmonic progression and none of them. 1/2^(n+1)

If a , b ,c are in harmonic progression, then the straight line ((x/a))+(y/b)+(1/c)=0 always passes through a fixed point. Find that point.