Question

In a geometric sequence t(10) = 63.41 and t(21) =618.16

Answer 1

`\begin{gathered} T_{10\text{ }}=ar^(n-1) \\ T_{10\text{ }}=ar^(10-1)\text{= 63.41} \\ ar^9\text{= 63.41}-----------(1) \\ T_{21\text{ }}=ar^(20) \\ ar^(20)\text{= 618.16}-----------(2) \\ (T_(21))/(T_(10))\text{ = }(618.16)/(63.41) \\ \\ (ar^(20))/(ar^9)\text{ = }(618.16)/(63.41) \\ r^(11)\text{ = 9.74} \\ \text{But from} \\ r^(11)\text{ = 9.74} \\ r^{9\text{ }}* r^2\text{ = 9.74} \\ 63.41\text{ }* r^2\text{ = 9.74} \\ r^2\text{ =}(9.74)/(63.41) \\ r^2\text{ = 0.1536} \\ r\text{ = }\sqrt[]{0.1536} \\ r\text{ = }0.391 \end{gathered}`