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{ =}(20)/(8)=\text{ }(10)/(4)=(5)/(2) \\ T_{10\text{ }}=ar^(n-1) \\ T_{10\text{ }}\text{ = 8 }*\text{ ( }(5)/(2))^(10-1) \\ \text{ = 8 }*\text{ ( }(5)/(2))^9 \\ =\text{ 8}*(1953125)/(512) \\ =8*3814.697 \\ =30517.578 \end{gathered}`