4. If A = (-4, -5) and B = (-1, -10), what is the length of segment AB? Round your answer to the nearest hundredth.

5.83095 or √34

Step-by-step explanation:

Find the difference between coordinates:

(x2-x1) = (-1 - -4) = 3

(y2-y1) = (-10 - -5) = -5

Square the results and sum them up:

(3)2 + (-5)2 = 9 + 25 = 34

Now Find the square root and that's your result:

Exact solution: √34 = √34

Approximate solution: 5.831

, 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