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Question
If in an infinite G.P., first term is equal to 10 times the sum of all successive terms, then its common ratio is
Options
1/10
1/11
1/9.
1/20
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Solution
\[\frac{1}{11}\]
Let the first term of the G.P. be a.
Let its common ratio be r.
According to the question, we have:
First term = 10 [Sum of all successive terms]
\[a = 10\left( \frac{ar}{1 - r} \right)\]
\[ \Rightarrow a - ar = 10ar\]
\[ \Rightarrow 11ar = a\]
\[ \Rightarrow r = \frac{a}{11a} = \frac{1}{11}\]
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