The equation for this sequence is:

a_n = a_n-1 + 3(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 + 3(6 - 1)
a₆ = 31 + 3(5)
a₆ = 46

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

-8z⁷ + 5z⁷
(-8 + 5)z⁷
-3z⁷

First, solve for \( \left|z + 5\right| \):

\( \left|z + 5\right| \) - 6 = 0
\( \left|z + 5\right| \) = 0 + 6
\( \left|z + 5\right| \) = 6

The value inside the absolute value brackets can be either positive or negative so (z + 5) must equal + 6 or -6 for \( \left|z + 5\right| \) to equal 6:

So, z = -11 or z = 1.

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 number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).