In a geometric progression, the first tern is 81 and the fourth term is 24. find the common ratio​

In a geometric progression, the first tern is 81 and the fourth term is 24. find the common ratio​

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  1. Hello,

    Let’s say a the  first term and r the ratio  of the G.P.

    [tex]u_1=a=81\\u_2=a*r\\u_3=a*r^2\\u_4=a*r^3\\\\\dfrac{u_4}{u_1} =\dfrac{a*r^3}{a} =r^3=\dfrac{24}{81} =\dfrac{8}{27} \\\\r=\sqrt[3]{\dfrac{8}{27} } \\\\\boxed{r=\dfrac{2}{3}}\\[/tex]

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