If the first and last terms of a geometric progression (G.P.) are 3 and 36, and r = 3, then the number of terms in the G.P. is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 6
In a G.P., the nth term is \(ar^{n-1}\), where a is the first term and r the common ratio. Setting it equal to the last term gives n.
Last term: \(3\times3^{n-1}=3^6\)
\(3^{n}=3^6\); the powers of the same base must be equal, so \(n=6\)