A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.

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:

\( \frac{3!}{5!} \)
\( \frac{3 \times 2 \times 1}{5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{5 \times 4} \)
\( \frac{1}{20} \)

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

2\( \sqrt{7} \) x 7\( \sqrt{7} \)
(2 x 7)\( \sqrt{7 \times 7} \)
14\( \sqrt{49} \)

Now we need to simplify the radical:

14\( \sqrt{49} \)
14\( \sqrt{7^2} \)
(14)(7)
98

The equation for this sequence is:

a_n = a_n-1 + 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 + 1
a₆ = 5 + 1
a₆ = 6