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 subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 4 and 8 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{7 x 2}{4 x 2} \) - \( \frac{4 x 1}{8 x 1} \)

\( \frac{14}{8} \) - \( \frac{4}{8} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{14 - 4}{8} \) = \( \frac{10}{8} \) = 1\(\frac{1}{4}\)

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.

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

8\( \sqrt{2} \) x 6\( \sqrt{9} \)
(8 x 6)\( \sqrt{2 \times 9} \)
48\( \sqrt{18} \)

Now we need to simplify the radical:

48\( \sqrt{18} \)
48\( \sqrt{2 \times 9} \)
48\( \sqrt{2 \times 3^2} \)
(48)(3)\( \sqrt{2} \)
144\( \sqrt{2} \)

There are 3 3-passenger taxis available so that's 3 x 3 = 9 total seats. There are 10 people needing transportation leaving 10 - 9 = 1 who will have to find other transportation.