Question

The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 16,4, 1, ... Find the 6th term.

Answer 1

The sequence above is a a geometric sequence . The common ratio between them is 0.25.

16, 4, 1

The sixth term of the sequence can be found below

`\begin{gathered} sixthterm=ar^(n-1) \\ \text{where} \\ r=\text{common ratio=0.25} \\ n=\text{ number of term} \\ a=first\text{ term=16} \\ \text{sixth term = 16}*0.25^(6-1) \\ \text{sixth term=16}*0.25^5 \\ \text{sixth term=16}*0.0009765625 \\ \text{sixth term=}0.015625 \\ \text{sixth term}\approx0.016 \end{gathered}`