It costs $74 per hour plus a $65 service fee to have a home theater system set up for you. Let t represent the number of hours. Which expression represents the total cost?

74t + 65= total cost

Step-by-step explanation:

74 is the amount per hour, so you would need to multiply that by the number of hours they work (74t) and the 65 is a set fee (does not change based on the amount of service) so you just add that on

, 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