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Question
Find :
the 12th term of the G.P.
\[\frac{1}{a^3 x^3}, ax, a^5 x^5 , . . .\]
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Solution
Here,
\[\text { First term, } a = \frac{1}{a^3 x^3}\]
\[\text { Common ratio }, r = \frac{a_2}{a_1} = \frac{ax}{\frac{1}{a^3 x^3}} = a^4 x^4 \]
\[ \therefore 12th \text { term } = a_{12} = a r^{(12 - 1)} = \frac{1}{a^3 x^3}( a^4 x^4 )^{11} = a^{41} x^{41} \]
\[\text { Thus, the 12th term of the given GP is } a^{41} x^{41} .\]
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