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Question
The 4th term of a G.P. is square of its second term, and the first term is − 3. Find its 7th term.
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Solution
\[\text { Let r be the common ratio of the given G . P } . \]
\[\text { Then }, a_4 = \left( a_2 \right)^2 \left[ \text { Given } \right]\]
\[\text { Now, }a r^3 = a^2 r^2 \]
\[ \Rightarrow r = a \]
\[ \Rightarrow r = - 3 \left[ \text { Putting } a = - 3 \right] \]
\[ \therefore a_7 = a r^6 \]
\[ \Rightarrow a_7 = \left( - 3 \right) \left( - 3 \right)^6 \left[ \text { Putting a = - 3 and }r = - 3 \right] \]
\[ \Rightarrow a_7 = \left( - 3 \right)\left( - 729 \right) \]
\[ \Rightarrow a_7 = - 2187\]
\[\text { Thus, the } 7^{th} \text { term of the G . P . is } - 2187 .\]
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