The equation for this sequence is:

a_n = a_n-1 + 6

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 + 6
a₆ = 25 + 6
a₆ = 31

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).

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

\( \frac{2}{8} \) ÷ \( \frac{3}{5} \) = \( \frac{2}{8} \) x \( \frac{5}{3} \)

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

\( \frac{2}{8} \) x \( \frac{5}{3} \) = \( \frac{2 x 5}{8 x 3} \) = \( \frac{10}{24} \) = \(\frac{5}{12}\)

The number of students taking German or Spanish is 15 + 13 = 28. Of that group of 28, 6 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 28 - 6 = 22 who are taking at least one language. 29 - 22 = 7 students who are not taking either language.

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:

\( \frac{4!}{2!} \)
\( \frac{4 \times 3 \times 2 \times 1}{2 \times 1} \)
\( \frac{4 \times 3}{1} \)
\( 4 \times 3 \)
12