For three weeks Mai kept a record of the number of students in front of her , x when she entered the lunch line and the time y in minutes until she sat down to eat

If 24 students are in front of Mai when she enters the lunch line about how long should Mai expect it to take until she sits down to eat

, 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