Question

If the 1st term of a G.P. is 2 and the 3rd term is 8, find the common ratio.

• A. 2
• B. 3
• C. 4
• D. 5

Hint:

For G.P., remember: \(a_n = a r^{n-1}\). Use given terms to form equations and solve for \(r\).

Answer 1

The Correct Option is A

Concept: In a Geometric Progression (G.P.), the \(n^{{th}}\) term is given by: \[ a_n = a \cdot r^{\,n-1} \]
Step 1: Use the given information.
First term: \[ a = 2 \] Third term: \[ a_3 = a \cdot r^2 = 8 \]
Step 2: Substitute values.
\[ 2 \cdot r^2 = 8 \Rightarrow r^2 = 4 \]
Step 3: Find \(r\).
\[ r = \pm 2 \] Since the options contain only positive values,
\[ r = 2 \]
Hence, the common ratio is 2.