Answer:
x is the number of months
Step-by-step explanation:
On the first run, hence after 0 months, Sean ran 0.5 miles or
[tex]0.5+2\cdot0 \quad \text{miles.}[/tex]
After 1 moth, Sean increased 2 miles to his run, hence during the first and second month, Sean ran 2.5 miles or
[tex]0.5+2=0.5+2\cdot1 \quad \text{miles.}[/tex]
After 2 moths, Sean increased 2 miles more to his run, hence during the second and third month, Sean ran 4.5 miles or
[tex]0.5+4=0.5+2+2=0.5+2\cdot2\quad\text{miles.}[/tex]
After 3 moths, Sean increased 2 miles more to his run, hence during the third and fourth month, Sean ran 6.5 miles or
[tex]0.5+6=0.5+4+2=0.5+2+2+2=0.5+2\cdot3 \quad \text{miles.}[/tex]
Using the same rule, we see that after x-months Sean will run
[tex]0.5+2\cdot x \quad \text{miles.}[/tex]
