Question

in a g.p. the second term and fifth term are 24 and 81 respectively find its nth term
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Answer 1

Step-by-step explanation:

${2}^{nd} term = 24 \\ a {r}^{1} = 24 \\ {5}^{th} term = 81 \\ a {r}^{4} = 81 \\ now \\ \frac{a {r}^{1} }{a {r}^{4} } = \frac{24}{81} \\ {r}^{ - 3} = \frac{8}{27} \\ {r}^{ - 3} = ( { \frac{3}{2} })^{ - 3} \\ r = \frac{3}{2} \\ now \\ ar = 24 \\ \frac{3a}{2} = 24 \\ a = 16 \\ {n}^{th} term = 16 \times ( { \frac{3}{2} })^{n - 1}$