Discussion
The first and last term of a G.P. are 7 and 448 respectively. If the sum is 889, then the common ratio is
Answer: B
The common ratio is 2.
For a G.P. with first term \(a\), last term \(l\) and ratio \(r\), the sum is \(S = \frac{lr - a}{r - 1}\). With \(a = 7\), \(l = 448\), \(S = 889\):
\[ \begin{aligned} \frac{448r - 7}{r - 1} &= 889 \\ 448r - 7 &= 889r - 889 \\ 441r &= 882 \Rightarrow r = 2 \end{aligned} \]
Check: 7, 14, 28, 56, 112, 224, 448 add up to 889. A ratio of 4 gives 7, 28, 112, 448 with sum 595, and ratios below 1 cannot go from 7 up to 448.
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