After last week's victory, he bought 2 medium pizzas and 1 large pizza, which is the perfect amount for the 9 players that got to come. This week, there were 33 players going, so he ordered 4 medium pizzas and 5 large pizzas, which was also the perfect amount of pizza needed. How many people does each size pizza feed?

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Step-by-step explanation:

, 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