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If the second term of a GP is 2 and the sum of its infinite term is 8, then the GP is
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Verified Answer
The correct answer is:
$4,2,1, \frac{1}{2}, \frac{1}{2^{2}}, \ldots . .$
Let the first term and common ratio of the G.P. is a and
r respectively.
$\begin{aligned} \text { Then, } a r=2, \frac{a}{1-r}=& 8 \\ \Rightarrow \quad \frac{a r}{r-r^{2}}=8 \quad \Rightarrow \quad 2=8 r-8 r^{2} \\ \Rightarrow \quad 4 r^{2}-4 r+1=0 \quad \Rightarrow \quad r=\frac{1}{2} \\ \therefore \text { GP. is } 4,2,1, \frac{1}{2}, \ldots . \end{aligned}$
r respectively.
$\begin{aligned} \text { Then, } a r=2, \frac{a}{1-r}=& 8 \\ \Rightarrow \quad \frac{a r}{r-r^{2}}=8 \quad \Rightarrow \quad 2=8 r-8 r^{2} \\ \Rightarrow \quad 4 r^{2}-4 r+1=0 \quad \Rightarrow \quad r=\frac{1}{2} \\ \therefore \text { GP. is } 4,2,1, \frac{1}{2}, \ldots . \end{aligned}$
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