The equation for this sequence is:

a_n = a_n-1 + 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 + 1
a₆ = 5 + 1
a₆ = 6

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40]. The first few multiples they share are [4, 8, 12, 16, 20] making 4 the smallest multiple 2 and 4 share.

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

\( \frac{6 x 2}{2 x 2} \) + \( \frac{4 x 1}{4 x 1} \)

\( \frac{12}{4} \) + \( \frac{4}{4} \)

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

\( \frac{12 + 4}{4} \) = \( \frac{16}{4} \) = 4

There are 3 5-passenger taxis available so that's 3 x 5 = 15 total seats. There are 18 people needing transportation leaving 18 - 15 = 3 who will have to find other transportation.

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

\( \frac{3}{8} \) x \( \frac{4}{8} \) = \( \frac{3 x 4}{8 x 8} \) = \( \frac{12}{64} \) = \(\frac{3}{16}\)

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.