Answer
The pattern $50$, $45$, $35$...
Could have both $20$ and $15$ as the next number.
Work Step by Step
We need to write a list of numbers that has two patterns so that the next number in the list can be $15$ or $20$.
There is more than one solution.
One solution would be:
$50$, $45$, $35$....
Here, we see that the second number is $5$ less than the first $(50-45=5)$.
We also see that the third number is $10$ less than the second $(45 - 35 =10)$
Inductively, we could both conclude that the next number is calculated by:
a. Subtracting $5$ more from the previous number to get this one than we did to get the previous number itself:
$50-5=45$ we subtracted $5$
$45-10=35$ we subtracted $5$ more, for $10$ total
This would make the next number:
$35-15=20$ (we subtract $5$ more, for $15$ in total)
b. Subtracting double what we previously subtracted:
$50-5=45$ we subtracted $5$
$45-10=35$ we subtracted $2*5=10$
This would make the next number:
$35-20=15$ (we subtracted $2*10=20$)
This means that the next number in the pattern could be $15$ or $20$.
