Rachel has 12 boston creme donuts and 6 glazed donuts to put in boxes. she wants each box to contain the same number of boston creme donuts and the same number of glazed donuts. what is the maximum number of boxes she can make? how many of each type of donut will each box contain?

6 boxes

2 boston creme donuts and 1 glazed donut per box

Step-by-step explanation:

She has 6 glazed donuts, so the maximum number of boxes is 6 by putting one glazed donut in each box since 6/6 = 1. Then she can put 2 boston cream donuts in each box since 12/6 = 2.

, 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