The equation for this sequence is:

a_n = a_n-1 + 2(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 + 2(6 - 1)
a₆ = 21 + 2(5)
a₆ = 31

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

\( \frac{20\sqrt{40}}{4\sqrt{8}} \)
\( \frac{20}{4} \) \( \sqrt{\frac{40}{8}} \)
5 \( \sqrt{5} \)

First, solve for \( \left|c - 7\right| \):

\( \left|c - 7\right| \) + 2 = -7
\( \left|c - 7\right| \) = -7 - 2
\( \left|c - 7\right| \) = -9

The value inside the absolute value brackets can be either positive or negative so (c - 7) must equal - 9 or --9 for \( \left|c - 7\right| \) to equal -9:

So, c = 16 or c = -2.

The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [10, 20, 30, 40, 50] making 10 the smallest multiple 2 and 10 have in common.

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.