Question

how do I Describe the pattern 18−9+4.5−2.25+...

Answer 1

Given the pattern

$18-9+4.5-2.25+\cdots$

To find the pattern,

If n is the first term, the pattern it followed is as follows

$n+(-\frac{1}{2})n+(-\frac{1}{2})(-\frac{1}{2})n+(-\frac{1}{2})(-\frac{1}{2})(-\frac{1}{2})n+\cdots$

$n-\frac{n}{2}+\frac{n}{4}-\frac{n}{8}+\frac{n}{16}-\frac{n}{32}+\cdots$

The first term of the given pattern is 18, i.e n = 18,

Substitute n into the pattern above,

$\begin{gathered} 18-\frac{18}{2}+\frac{18}{4}-\frac{18}{8}+\frac{18}{16}-\frac{18}{32}+\cdots \\ =18-9+4.5-2.25+1.125-0.5625+\cdots \end{gathered}$

Hence, the pattern is

$n-\frac{n}{2}+\frac{n}{4}-\frac{n}{8}+\frac{n}{16}-\frac{n}{32}+\cdots$