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Question
If second term of a G.P. is 2 and the sum of its infinite terms is 8, then its first term is
Options
(a) 1/4
(b) 1/2
(c) 2
(d) 4
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Solution
(d) 4
\[a_2 = 2 \]
\[ \therefore ar = 2 . . . . . . . . (i)\]
\[\text{ Also }, S_\infty = 8\]
\[ \Rightarrow \frac{a}{\left( 1 - r \right)} = 8\]
\[ \Rightarrow \frac{a}{\left( 1 - \frac{2}{a} \right)} = 8 \left[ \text{ Using } (i) \right]\]
\[ \Rightarrow a^2 = 8\left( a - 2 \right)\]
\[ \Rightarrow a^2 - 8a + 16 = 0\]
\[ \Rightarrow \left( a - 4 \right)^2 = 0\]
\[ \Rightarrow a = 4\]
\[\]
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