Luca packed 5 shirts and 2 pairs of pants for a two-day trip. if he keeps the same ratio of shirts to number of days, how many shirts should he pack for a twelve-day trip?

  30 shirts

Step-by-step explanation:

A 12-day trip is 6 times as long as a 2-day trip, so he should pack 6 times as many shirts:

  6 × 5 shirts = 30 shirts

Luca should pack 30 shirts for his 12-day trip.

, 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