The equation for this sequence is:

a_n = a_n-1 + 3(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 + 3(6 - 1)
a₆ = 31 + 3(5)
a₆ = 46

To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.

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

6\( \sqrt{125} \) - 9\( \sqrt{5} \)
6\( \sqrt{25 \times 5} \) - 9\( \sqrt{5} \)
6\( \sqrt{5^2 \times 5} \) - 9\( \sqrt{5} \)
(6)(5)\( \sqrt{5} \) - 9\( \sqrt{5} \)
30\( \sqrt{5} \) - 9\( \sqrt{5} \)

Now that the radicands are identical, you can subtract them:

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{25}{4}} \)
\( \frac{\sqrt{25}}{\sqrt{4}} \)
\( \frac{\sqrt{5^2}}{\sqrt{2^2}} \)
\( \frac{5}{2} \)
2\(\frac{1}{2}\)

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 + 50.2km + 12.2km
total distance = 62.9km