The equation for this sequence is:

a_n = a_n-1 + 3

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
a₆ = 13 + 3
a₆ = 16

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.

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

6\( \sqrt{5} \) x 9\( \sqrt{3} \)
(6 x 9)\( \sqrt{5 \times 3} \)
54\( \sqrt{15} \)

To simplify this fraction, first find the greatest common factor between them. The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]. They share 6 factors [1, 2, 4, 5, 10, 20] making 20 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{20}{60} \) = \( \frac{\frac{20}{20}}{\frac{60}{20}} \) = \( \frac{1}{3} \)

First, solve for \( \left|c + 4\right| \):

\( \left|c + 4\right| \) + 7 = -5
\( \left|c + 4\right| \) = -5 - 7
\( \left|c + 4\right| \) = -12

The value inside the absolute value brackets can be either positive or negative so (c + 4) must equal - 12 or --12 for \( \left|c + 4\right| \) to equal -12:

So, c = 8 or c = -16.