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+(-(1)/(2))n+(-(1)/(2))(-(1)/(2))n+(-(1)/(2))(-(1)/(2))(-(1)/(2))n+\cdots`

`n-(n)/(2)+(n)/(4)-(n)/(8)+(n)/(16)-(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-(18)/(2)+(18)/(4)-(18)/(8)+(18)/(16)-(18)/(32)+\cdots \\ =18-9+4.5-2.25+1.125-0.5625+\cdots \end{gathered}`

Hence, the pattern is

`n-(n)/(2)+(n)/(4)-(n)/(8)+(n)/(16)-(n)/(32)+\cdots`