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 divide fractions, invert the second fraction and then multiply:

\( \frac{3}{7} \) ÷ \( \frac{1}{9} \) = \( \frac{3}{7} \) x \( \frac{9}{1} \)

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

\( \frac{3}{7} \) x \( \frac{9}{1} \) = \( \frac{3 x 9}{7 x 1} \) = \( \frac{27}{7} \) = 3\(\frac{6}{7}\)

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.

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{32}{12} \) = 2\(\frac{2}{3}\)

So, it will take 2 full vans and one partially full van to transport the entire team making a total of 3 vans.

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:

-3c⁴ x 6c³
(-3 x 6)c^{(4 + 3)}
-18c⁷