Astudent wrote the first three values in a geometric sequence as shown below.
f, g,
which of the following shows the correct relationship between these terms?

a. f-g=g-h
b. fg=gh
c. h=g/f
d. h=g^2/f

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)