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Question
Find the 4th term from the end of the G.P.
\[\frac{1}{2}, \frac{1}{6}, \frac{1}{18}, \frac{1}{54}, . . . , \frac{1}{4374}\]
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Solution
\[\text { After reversing the given G . P . , we get another G . P . whose first term, l is } \frac{1}{4374} \text { and common ratio is } 3 . \]
\[ \therefore 4^{th} \text { term from the end } = l \left( \frac{1}{r} \right)^{4 - 1} \]
\[ = \left( \frac{1}{4374} \right) \left( 3 \right)^{4 - 1} \]
\[ = \left( \frac{27}{4374} \right)\]
\[ = \frac{1}{162}\]
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