Find the distance between the points (1,8) and (7, 16).

The first number on a given pair of coordinates is the x coordinate, while the second number is always the y coordinate (there is also a z coordinate, but we don't have to worry about that as the z coordinate is never in the question). To find the distance of the two coordinates on the x axis, we subtract the second x coordinate from the first x coordinate. 1-7=-6. So we now know the x coordinate distance between the two is 6. To find the distance of the two coordinates on the y axis, we subtract the second y coordinate from the first y coordinate. 8-16=-8, So we now know the y coordinate between the two is 8.

And so, the distance between the two coordinates is (6,8).

b

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