Discussion
The sum of first n terms of a G.P. is 1023. If the first term is 1 and the common ratio is 2, then the value of n is
Answer: C
The value is n = 10.
The sum of n terms of a G.P. with first term a and ratio r is \(\frac{a(r^{n} - 1)}{r - 1}\).
\[ \begin{aligned} \frac{1(2^{n} - 1)}{2 - 1} &= 1023 \\ 2^{n} &= 1024 = 2^{10} \end{aligned} \]
So n = 10. n = 11 would give 2047 and n = 9 would give 511; the slip is usually to take \(2^{n} = 1023\) and round up.
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