To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] 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 [24, 48, 72, 96] making 24 the smallest multiple 6 and 8 share.

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

\( \frac{8 x 4}{6 x 4} \) + \( \frac{3 x 3}{8 x 3} \)

\( \frac{32}{24} \) + \( \frac{9}{24} \)

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

\( \frac{32 + 9}{24} \) = \( \frac{41}{24} \) = 1\(\frac{17}{24}\)

1

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 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 have in common.

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{9 + 3 + 9 + 3}{4} \) = \( \frac{24}{4} \) = 6