Question

The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).8,20,50,...Find the 10th term.

Answer 1

$\begin{gathered} \text{This is a Geometry progression } \\ n\text{ = 10} \\ a\text{ = 8} \\ r\text{ =}\frac{20}{8}=\text{ }\frac{10}{4}=\frac{5}{2} \\ T_{10\text{ }}=ar^{n-1} \\ T_{10\text{ }}\text{ = 8 }\times\text{ ( }\frac{5}{2})^{10-1} \\ \text{ = 8 }\times\text{ ( }\frac{5}{2})^9 \\ =\text{ 8}\times\frac{1953125}{512} \\ =8\times3814.697 \\ =30517.578 \end{gathered}$