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.

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

7\( \sqrt{3} \) x 5\( \sqrt{6} \)
(7 x 5)\( \sqrt{3 \times 6} \)
35\( \sqrt{18} \)

Now we need to simplify the radical:

35\( \sqrt{18} \)
35\( \sqrt{2 \times 9} \)
35\( \sqrt{2 \times 3^2} \)
(35)(3)\( \sqrt{2} \)
105\( \sqrt{2} \)

To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

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

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

\( \frac{11 + 9 + 13 + 7}{4} \) = \( \frac{40}{4} \) = 10