Question

If the first and fourth terms of a GP are 1 and 27 respectively, then the common ratio is

• A. 2
• B. 4
• C. 3
• D. 6

Answer 1

The Correct Option is C

The general form of the \(n\)-th term of a geometric progression (GP) is given by: \[ T_n = ar^{n-1} \] where \(a\) is the first term and \(r\) is the common ratio. From the question: - The first term \(T_1 = 1\) so, \(a = 1\). - The fourth term \(T_4 = 27\), so we have the equation: \[ T_4 = ar^{4-1} = ar^3 = 27 \] Substituting \(a = 1\): \[ r^3 = 27 \] Taking the cube root of both sides: \[ r = \sqrt[3]{27} = 3 \]

The correct option is (C): \(3\)