The equation for this sequence is:

a_n = a_n-1 + 3(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 + 3(6 - 1)
a₆ = 31 + 3(5)
a₆ = 46

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

2 + (5 + 4) ÷ 2 x 4 - 2²
P: 2 + (9) ÷ 2 x 4 - 2²
E: 2 + 9 ÷ 2 x 4 - 4
MD: 2 + \( \frac{9}{2} \) x 4 - 4
MD: 2 + \( \frac{36}{2} \) - 4
AS: \( \frac{4}{2} \) + \( \frac{36}{2} \) - 4
AS: \( \frac{40}{2} \) - 4
AS: \( \frac{40 - 8}{2} \)
\( \frac{32}{2} \)
16

You have 13 out of the total of 450 raffle tickets sold so you have a (\( \frac{13}{450} \)) x 100 = \( \frac{13 \times 100}{450} \) = \( \frac{1300}{450} \) = 3% chance to win the raffle.

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{21\sqrt{12}}{3\sqrt{4}} \)
\( \frac{21}{3} \) \( \sqrt{\frac{12}{4}} \)
7 \( \sqrt{3} \)

25% of the water consumption is industrial use and 10% is personal use so (25% - 10%) = 15% more water is used for industrial purposes. 45,000 gallons are consumed daily so industry consumes \( \frac{15}{100} \) x 45,000 gallons = 6,750 gallons.