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

The number of students taking German or Spanish is 8 + 13 = 21. Of that group of 21, 2 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 21 - 2 = 19 who are taking at least one language. 31 - 19 = 12 students who are not taking either language.

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

\( \frac{4}{6} \) ÷ \( \frac{1}{5} \) = \( \frac{4}{6} \) x \( \frac{5}{1} \)

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

\( \frac{4}{6} \) x \( \frac{5}{1} \) = \( \frac{4 x 5}{6 x 1} \) = \( \frac{20}{6} \) = 3\(\frac{1}{3}\)

Diane scored 98% on the test meaning she earned 98% of the possible points on the test. There were 240 possible points on the test so she earned 240 x 0.98 = 234 points. Each question is worth 3 points so she got \( \frac{234}{3} \) = 78 questions right.

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

8c⁶ x 6c⁶
(8 x 6)c^{(6 + 6)}
48c¹²