A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.

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:

\( \frac{6!}{3!} \)
\( \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1} \)
\( \frac{6 \times 5 \times 4}{1} \)
\( 6 \times 5 \times 4 \)
120

The greatest common factor (GCF) is the greatest factor that divides two integers.

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

3\( \sqrt{175} \) + 8\( \sqrt{7} \)
3\( \sqrt{25 \times 7} \) + 8\( \sqrt{7} \)
3\( \sqrt{5^2 \times 7} \) + 8\( \sqrt{7} \)
(3)(5)\( \sqrt{7} \) + 8\( \sqrt{7} \)
15\( \sqrt{7} \) + 8\( \sqrt{7} \)

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

The equation for this sequence is:

a_n = a_n-1 + 4

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 + 4
a₆ = 17 + 4
a₆ = 21