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Question
The fourth term of a G.P. is 27 and the 7th term is 729, find the G.P.
Solution
\[\text { Let a be the first term and r be the common ratio of the given G . P }. \]
\[ \therefore a_{4 =} 27 \text { and } a_7 = 729\]
\[ \Rightarrow a r^3 = 27 \text { and }a r^6 = 729\]
\[ \Rightarrow \frac{a r^6}{a r^3} = \frac{729}{27}\]
\[ \Rightarrow r^3 = 3^3 \]
\[ \Rightarrow r = 3\]
\[\text { Putting } r = 3\text { in a } r^3 = 27\]
\[a \left( 3 \right)^3 = 27 \]
\[ \Rightarrow a = 1\]
\[\text { Thus, the given G . P . is } 1, 3, 9, . . . \]
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