Discussion
The product of first four terms of a G.P. is 324 and the product of first three terms of the G.P. is 216. Then the first term is
Answer: E
The first term is 12.
Write the terms as \(a, ar, ar^{2}, ar^{3}\). Dividing the product of four terms by the product of three leaves the fourth term:
\[ \begin{aligned} ar^{3} &= \frac{324}{216} = \frac{3}{2} \\ a^{3}r^{3} &= 216, \quad ar = 6 \\ r^{2} &= \frac{ar^{3}}{ar} \\ &= \frac{1}{4}, \quad r \\ &= \frac{1}{2} \\ a &= \frac{6}{r} = 12 \end{aligned} \]
Check: the terms are 12, 6, 3, 1.5, with products \(12 \times 6 \times 3 = 216\) and \(216 \times 1.5 = 324\). 6 is the second term \(ar\), and 3 is the third.
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