The equation for this sequence is:

a_n = a_n-1 + 4(n - 1)

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 4(6 - 1)
a₆ = 41 + 4(5)
a₆ = 61

You have 14 out of the total of 350 raffle tickets sold so you have a (\( \frac{14}{350} \)) x 100 = \( \frac{14 \times 100}{350} \) = \( \frac{1400}{350} \) = 4% chance to win the raffle.

To fill a 20 gallon tank exactly halfway you'll need 10 gallons of fuel. Each fuel can holds 2 gallons so:

cans = \( \frac{10 \text{ gallons}}{2 \text{ gallons}} \) = 5

A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 20 workers at the company now and that's enough to staff 5 crews so there are \( \frac{20}{5} \) = 4 workers on a crew. 9 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 9 x 4 = 36 total workers to staff the crews during the busy season. The company already employs 20 workers so they need to add 36 - 20 = 16 new staff for the busy season.