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The 2nd term of an exponential sequence is 9 while the 4th term is 81. Find the common ratio, the first and the sum of the first five terms​

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PTCharm

Apply the general formula to solve

[tex]ar = 9 \\ a {r}^{3} = 81 \\ \frac{{ar}^{3} }{ar} = \frac{81}{9} \\ {r}^{2} = 9 \\ r = 3 \: \\ therefore \: a = 3[/tex]

Then, use the sum formula

[tex] \frac{a( {r}^{n} - 1) }{r - n} \\ \frac{3( {3}^{5} - 1)}{3 - 1} = 363[/tex]

Hope this helps!

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