Students spin a spinner 500 times. the table shows the results of their experiment.
purple- 100 times
white- 200 times
blue-150 times
pink- 50 times
based on the results, predict the number of times the spinner will land on blue in 100 spins.

, 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