Discussion
What term of the G.P. \(2, 1, 1/2, 1/4, ...\) is 1/128?
Answer: B
Here, \(a=2, r=1/2, a_n=1/128\). Using the formula \(a_n = ar^{n-1}\): \(1/128 = 2 \times (1/2)^{n-1} \Rightarrow 1/256 = (1/2)^{n-1}\). Since \(256 = 2^8\), we have \((1/2)^8 = (1/2)^{n-1}\). Equating powers: \(8=n-1 \Rightarrow n=9\). It is the 9th term.
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