(-4,-8) and( 3,6) slope

would be the slope of a line that goes between and .

Step-by-step explanation:

Given a line that goes through two points, and (,) the slope of this line would be equal to the "rise over run" between these two points.

"Rise" refers to the change in the -coordinate between the two points, . Similarly, "run" refers to the change in the -coordinate, .

.

For , the -coordinate is and the -coordinate is .

For , the -coordinate is and the -coordinate is .

The "rise" between these two points would be .

The "run" between these two points would be .

Thus, the slope of a line that goes through the two points would be:

.

, 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