What is the geometric mean of the data 2, 4, 8,16, 32?

Question

Question

Answer 1

Concept:

The geometric mean of the numbers a₁, a₂,...,a_n is given by ⇔ G = \(\rm (a_1\times a_2\cdots \times a_n)^{\frac 1 n}\)

Calculation:

GIven data: 2, 4, 8,16, 32?

Geometric mean = \((2 \times 4 \times8 \times 16 \times 32)^{\frac 1 5}\)

\(=(2^1 \times 2^2\times 2^3\times 2^4\times 2^5)^{\frac1 5}\)

\(=(2^{15})^{\frac1 5}\)

= 2³

= 8

Hence, option (3) is correct.