Question

The product of the first five terms of a GP is 32. What is the 3rd term?

• A. 4
• B. 2
• C. 8
• D. 16

Hint:

In a geometric progression, the product of the terms depends on the first term and the common ratio. The nth term is given by \( ar^{n-1} \).

Answer 1

The Correct Option is C

Let the terms of the geometric progression be \( a, ar, ar^2, ar^3, ar^4 \), where: - \( a \) is the first term, - \( r \) is the common ratio. The product of the first five terms is given by: \[ a \times ar \times ar^2 \times ar^3 \times ar^4 = a^5 r^{10} \] We are told that the product of the first five terms is 32, so: \[ a^5 r^{10} = 32 \] Taking the fifth root of both sides: \[ a r^2 = 2 \] The 3rd term is \( ar^2 \), which is
2. Thus, the correct answer is \( 8 \).