Discussion
The product of first 5 terms of a G.P., whose terms are increasing, is 32. The third term of the G.P. is
Answer: A
The third term is 2.
Write the five terms as \(\frac{a}{r^{2}}, \frac{a}{r}, a, ar, ar^{2}\), where \(a\) is the third term. Their product is \(a^{5}\), because the powers of \(r\) cancel:
\[ a^{5} = 32 = 2^{5} \Rightarrow a = 2 \]
The ratio does not matter (the word increasing only says \(r \gt 1\)). 4 and 8 would give products \(4^{5}\) and \(8^{5}\); 1/2 and 1/8 would give products less than 1.
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