Afreight train is carrying goods across the country. the distance it has traveled varies directly with the number of gallons of fuel it has used. see the graph below.

Step-by-step explanation:

The train uses

If you reduce that you get that the train uses

To find the slope of the line, we will use the 2 points on the coordinate plane where the graph goes through:  (0, 0) and (400, 200)

Applying the slope formula:

answer: it's upside down and i can't read it

step-by-step explanation:

, 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