Ms. Roofe is making cookies. The recipe uses 2/3 cup of chocolate chips for each batch of cookies. If Ms. Roofe has 7 1/2 cups of chocolate chips, what is the maximum number of full batches of cookies that Ms. Roofe can make?

answer: 414,377,008

step-by-step explanation:

just multiply it

, 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