To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 16 are [16, 32, 48, 64, 80, 96]. The first few multiples they share are [16, 32, 48, 64, 80] making 16 the smallest multiple 8 and 16 share.

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

\( \frac{6 x 2}{8 x 2} \) + \( \frac{3 x 1}{16 x 1} \)

\( \frac{12}{16} \) + \( \frac{3}{16} \)

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

\( \frac{12 + 3}{16} \) = \( \frac{15}{16} \) = \(\frac{15}{16}\)

To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 500 meters to kilometers, divide the distance by 1000 to get 0.5km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.5km + 30.5km + 9.5km
total distance = 40.5km

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:

6a⁵ x 3a²
(6 x 3)a^{(5 + 2)}
18a⁷

The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] and the factors of 32 are [1, 2, 4, 8, 16, 32]. They share 4 factors [1, 2, 4, 8] making 8 the greatest factor 40 and 32 have in common.

The equation for this sequence is:

a_n = a_n-1 + 5

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 + 5
a₆ = 21 + 5
a₆ = 26