Kyle has been hired to decorate a ballroom for a special event. to decorate the ballroom, he needs 300 balloons. the balloons come in packages of 25. kyle already has 75 balloons from a previous special event. how many packages should he purchase to meet the 300 balloon requirement?

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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

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