The equation for this sequence is:

a_n = a_n-1 + 5

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 + 5
a₆ = 21 + 5
a₆ = 26

54% of the water consumption is industrial use and 32% is personal use so (54% - 32%) = 22% more water is used for industrial purposes. 30,000 gallons are consumed daily so industry consumes \( \frac{22}{100} \) x 30,000 gallons = 6,600 gallons.

To add these radicals together their radicands must be the same:

2\( \sqrt{112} \) + 2\( \sqrt{7} \)
2\( \sqrt{16 \times 7} \) + 2\( \sqrt{7} \)
2\( \sqrt{4^2 \times 7} \) + 2\( \sqrt{7} \)
(2)(4)\( \sqrt{7} \) + 2\( \sqrt{7} \)
8\( \sqrt{7} \) + 2\( \sqrt{7} \)

Now that the radicands are identical, you can add them together:

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{5!}{2!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1} \)
\( \frac{5 \times 4 \times 3}{1} \)
\( 5 \times 4 \times 3 \)
60