Acompany rents out 15 food booths and 20 game booths at the county fair. the fee for a food booth is $100 plus $5 per day. the fee for a game booth is $50 plus $7 per day. the fair lasts for 'd' days, and all the booths are rented for the entire time. write and simplify an expression for the amount in dollars the the company is paid.

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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