Naomi plans to attend a four-year college that costs a total of $21,800 per year. Her family invests $9,500 in an account that earns 6% annual interest compounded monthly. If Naomi’s family invests an additional $450 per month for five years, will the value of the account be enough to pay for at least the first two years of college? Use an online periodic deposit calculator.

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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