Question

Which pattern could have been used to create the sequence? 500, –100, 20, –4

Answer 1

First, we are going to simplify the fractions into ratios using this formula:

`r=(a_n)/(a_(n-1))`
So...

`(-100)/(500)=-(1)/(5),\:\quad (20)/(-100)=-(1)/(5),\:\quad (-4)/(20)=-(1)/(5)`
The sequence is geometric. Since we have to multiply the number by
`- (1)/(5)` to get the next number.

If the first element of the sequence is 500, the next one is calculated by:

`n=500\left(-(1)/(5)\right)`

Have nice day! :)