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

\( \frac{8 + 4 + 8 + 4}{4} \) = \( \frac{24}{4} \) = 6

A ratio of 5:1 means that there are 5 home fans for every one visiting fan. So, of every 6 fans, 5 are home fans and \( \frac{5}{6} \) of every fan in the stadium is a home fan:

43,000 fans x \( \frac{5}{6} \) = \( \frac{215000}{6} \) = 35,833 fans.

The equation for this sequence is:

a_n = a_n-1 + 4

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 + 4
a₆ = 17 + 4
a₆ = 21

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:

\( \frac{5 x 2}{2 x 2} \) + \( \frac{4 x 1}{4 x 1} \)

\( \frac{10}{4} \) + \( \frac{4}{4} \)

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

\( \frac{10 + 4}{4} \) = \( \frac{14}{4} \) = 3\(\frac{1}{2}\)

A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.