For the dinner special at a restaurant, the customer must choose an appetizer, a salad, an entree, a side dish, and a dessert. here are the items to choose from. appetizer chicken strips, onion rings, buffalo wings salad caesar, garden entree salmon, lamb, roast turkey, grilled chicken side dish corn, mixed vegetables, pinto beans dessert cheesecake, chocolate cake, ice cream, brownies how many dinner specials are possible?

there is no

, 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