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

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 200 meters to kilometers, divide the distance by 1000 to get 0.2km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.2km + 20.5km + 7.6000000000000005km
total distance = 28.3km

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:

42,000 fans x \( \frac{5}{6} \) = \( \frac{210000}{6} \) = 35,000 fans.

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.

To add these radicals together their radicands must be the same:

7\( \sqrt{8} \) + 4\( \sqrt{2} \)
7\( \sqrt{4 \times 2} \) + 4\( \sqrt{2} \)
7\( \sqrt{2^2 \times 2} \) + 4\( \sqrt{2} \)
(7)(2)\( \sqrt{2} \) + 4\( \sqrt{2} \)
14\( \sqrt{2} \) + 4\( \sqrt{2} \)

Now that the radicands are identical, you can add them together: