The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

To simplify this fraction, first find the greatest common factor between them. The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 68 are [1, 2, 4, 17, 34, 68]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{36}{68} \) = \( \frac{\frac{36}{4}}{\frac{68}{4}} \) = \( \frac{9}{17} \)

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

\( \frac{45\sqrt{25}}{9\sqrt{5}} \)
\( \frac{45}{9} \) \( \sqrt{\frac{25}{5}} \)
5 \( \sqrt{5} \)

To divide fractions, invert the second fraction and then multiply:

\( \frac{2}{9} \) ÷ \( \frac{1}{9} \) = \( \frac{2}{9} \) x \( \frac{9}{1} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{2}{9} \) x \( \frac{9}{1} \) = \( \frac{2 x 9}{9 x 1} \) = \( \frac{18}{9} \) = 2

The equation for this sequence is:

a_n = a_n-1 + 7

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 + 7
a₆ = 29 + 7
a₆ = 36