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Question
The seventh term of a G.P. is 8 times the fourth term and 5th term is 48. Find the G.P.
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Solution
\[\text { Let a be the first term and r be the common ratio }. \]
\[ \therefore a_7 = 8 a_4 \text { and } a_5 = 48\]
\[ \Rightarrow a r^6 = 8a r^3 \text { and } a r^4 = 48\]
\[ \Rightarrow r^3 = 8 \]
\[ \Rightarrow r^3 = 2^3 \]
\[ \Rightarrow r = 2\]
\[\text { Putting r } = 2 \text { in a }r^4 = 48\]
\[a \left( 2 \right)^4 = 48 \]
\[ \Rightarrow a = 3\]
\[\text { Thus, the given G . P . is } 3, 6, 12, . . . \]
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