Answer – D. h = g^2/f
EXPLANATIONIn mathematics a geometric sequence consists of a sequence of numbers where the next term is found by multiplying the previous term by a fixed, non-zero number. This fixed number is called the common ratio.
Therefore, Given the Geometric sequence f, g, h
Let the common ratio be ‘r’
f(r) = g … (Equation I)
g(r) = h … (Equation II)
Make ‘r’ the subject of both equations
f(r) = g … (Equation I)
r = g/f … (Equation III)
g(r) = h … (Equation II)
r = h/g … (Equation IV)
Since r = g/f (Equation III), substitute g/f for ‘r’ in Equation IV
r = h/g … (Equation IV)
g/f = h/g … (Equation V)
Multiply both sides of Equation V by ‘g’
g/f = h/g … (Equation V)
g/f X g = h/g X g
g^2/f = h
h = g^2/f … (ANSWER)
