Part one: you have been asked to build a scale model of your school out of toothpicks. imagine your school is 30 feet tall. your scale is 1 ft: 1.68 cm. if a toothpick is 6.3 cm tall, how many toothpicks tall will your model be? part two: your mother is out of toothpicks, and suggests you use cotton swabs instead. you measure them, and they are 7.2 cm tall. how many cotton swabs tall will your model be? if necessary, round your answer to the nearest whole number.

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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

, and for