If 1, x, y, z, 16 are in geometric progression, then what is the value of x+y+z ?

If 5, x, y, z, 405 are the first five terms of a geometric progression, find the values of x, y, and z.

Three positive distinct numbers x, y, z are three terms of geometric progression in an order and the numbers x + y, y + z, z + x are three terms of arithmetic progression in that order. Prove that x^x . y^y = x^y . Y^z . Z^x .

If x^(y^(z))=1, y^(z^(x))=125 and Z^(y^(x))=243 (x,y and z are natural numbers), then what is the value of 9x+10y-18z ?

Three positive distinct numbers x,y,z are three terms of geometric progression in an order , and the number x+y,y+z,z+x are three terms of arithmetic progression in that order . Prove that x^(x).y^(y).z^(z)=x^(y).y^(z).z^(x)

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.