Discussion
The sum of the first and third term of a G.P. is 20 and the sum of the first three terms is 26. Find the common ratio.
Answer: D
Let the terms be \(a, ar, ar^2\). Given \(a+ar^2=20 \Rightarrow a(1+r^2)=20\). And \(a+ar+ar^2=26 \Rightarrow a(1+r+r^2)=26\). Dividing the second eq by the first: \(\frac{1+r+r^2}{1+r^2} = \frac{26}{20} = \frac{13}{10}\). \(10+10r+10r^2 = 13+13r^2 \Rightarrow 3r^2-10r+3=0 \Rightarrow (3r-1)(r-3)=0\). So \(r=3\) or \(r=1/3\).
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