Question

If a, b, c are in G.P. then \(\frac{a}{b}=\)

• A. \(\frac{b}{c}\)
• B. \(\frac{c}{b}\)
• C. \(\frac{b}{a}\)
• D. \(\frac{c}{a}\)

Answer 1

The Correct Option is A

Step 1: Understand what it means for \( a, b, c \) to be in G.P.

If three numbers are in Geometric Progression, then:

\[ \frac{b}{a} = \frac{c}{b} \]

Step 2: Cross-multiply the equation.

\[ b^2 = a \cdot c \]

Step 3: Divide both sides by \( b \cdot c \)

\[ \frac{b^2}{b \cdot c} = \frac{a \cdot c}{b \cdot c} \]

\[ \frac{b}{c} = \frac{a}{b} \]

Step 4: Hence, we get:

\[ \frac{a}{b} = \frac{b}{c} \]

The correct option is (A): \(\frac{b}{c}\)