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

The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 24 meters so the equation becomes: 2w + 2h = 24.

Putting these two equations together and solving for width (w):

2w + 2h = 24
w + h = \( \frac{24}{2} \)
w + h = 12
w = 12 - h

From the question we know that h = 2w so substituting 2w for h gives us:

w = 12 - 2w
3w = 12
w = \( \frac{12}{3} \)
w = 4

Since h = 2w that makes h = (2 x 4) = 8 and the area = h x w = 4 x 8 = 32 m²

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

3\( \sqrt{48} \) + 8\( \sqrt{3} \)
3\( \sqrt{16 \times 3} \) + 8\( \sqrt{3} \)
3\( \sqrt{4^2 \times 3} \) + 8\( \sqrt{3} \)
(3)(4)\( \sqrt{3} \) + 8\( \sqrt{3} \)
12\( \sqrt{3} \) + 8\( \sqrt{3} \)

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

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

4 + (2 + 2) ÷ 4 x 4 - 4²
P: 4 + (4) ÷ 4 x 4 - 4²
E: 4 + 4 ÷ 4 x 4 - 16
MD: 4 + \( \frac{4}{4} \) x 4 - 16
MD: 4 + \( \frac{16}{4} \) - 16
AS: \( \frac{16}{4} \) + \( \frac{16}{4} \) - 16
AS: \( \frac{32}{4} \) - 16
AS: \( \frac{32 - 64}{4} \)
\( \frac{-32}{4} \)
-8

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $600
i = 0.05 x $600
i = $30