Discussion
The fifth term of a G.P. is 81 and the second term is 24. Find the G.P.
Answer: A
We have \(a_5 = ar^4 = 81\) and \(a_2 = ar = 24\). Dividing the equations: \(\frac{ar^4}{ar} = \frac{81}{24} \Rightarrow r^3 = 27/8\). So, \(r=3/2\). Substitute r back into the second equation: \(a(3/2) = 24 \Rightarrow a = 24 \times 2/3 = 16\). The G.P. is 16, \(16 \times 3/2 = 24\), \(24 \times 3/2 = 36\), ...
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