The equation for this sequence is:

a_n = a_n-1 + 2

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 + 2
a₆ = 9 + 2
a₆ = 11

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

5 + (4 + 3) ÷ 3 x 3 - 3²
P: 5 + (7) ÷ 3 x 3 - 3²
E: 5 + 7 ÷ 3 x 3 - 9
MD: 5 + \( \frac{7}{3} \) x 3 - 9
MD: 5 + \( \frac{21}{3} \) - 9
AS: \( \frac{15}{3} \) + \( \frac{21}{3} \) - 9
AS: \( \frac{36}{3} \) - 9
AS: \( \frac{36 - 27}{3} \)
\( \frac{9}{3} \)
3

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{18 + 12 + 18 + 12}{4} \) = \( \frac{60}{4} \) = 15

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).

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

8\( \sqrt{75} \) + 4\( \sqrt{3} \)
8\( \sqrt{25 \times 3} \) + 4\( \sqrt{3} \)
8\( \sqrt{5^2 \times 3} \) + 4\( \sqrt{3} \)
(8)(5)\( \sqrt{3} \) + 4\( \sqrt{3} \)
40\( \sqrt{3} \) + 4\( \sqrt{3} \)

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