Hank ran from his home 3 miles south, 2 miles west and 4.5 miles north and then ran in a direct path back to his house. draw a model to represent this situation

Step-by-step explanation:

Pick a point to be home

Go 3 miles south (down from home)

Go 2 miles west (left)

Go 4.5 miles north (up)

Back to home from there

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

5

step-by-step explanation: