In a geometric progression, the first tern is 81 and the fourth term is 24. find the common ratio July 31, 2021 by Thu Thảo In a geometric progression, the first tern is 81 and the fourth term is 24. find the common ratio

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] Reply

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]

Step-by-step explanation:81/24= 27/8