The equation for this sequence is:

a_n = a_n-1 + 6

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 + 6
a₆ = 25 + 6
a₆ = 31

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{60}{100} \) = \( \frac{60 x 25}{100} \) = \( \frac{1500}{100} \) = 15 shots

The center makes 45% of his shots so he'll have to take:

shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)

to make as many shots as the guard. Plugging in values for the center gives us:

center shots taken = \( \frac{15}{\frac{45}{100}} \) = 15 x \( \frac{100}{45} \) = \( \frac{15 x 100}{45} \) = \( \frac{1500}{45} \) = 33 shots

to make the same number of shots as the guard and thus score the same number of points.

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 fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [20, 40, 60, 80] making 20 the smallest multiple 4 and 10 share.

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

\( \frac{9 x 5}{4 x 5} \) + \( \frac{7 x 2}{10 x 2} \)

\( \frac{45}{20} \) + \( \frac{14}{20} \)

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

\( \frac{45 + 14}{20} \) = \( \frac{59}{20} \) = 2\(\frac{19}{20}\)

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

8\( \sqrt{12} \) + 2\( \sqrt{3} \)
8\( \sqrt{4 \times 3} \) + 2\( \sqrt{3} \)
8\( \sqrt{2^2 \times 3} \) + 2\( \sqrt{3} \)
(8)(2)\( \sqrt{3} \) + 2\( \sqrt{3} \)
16\( \sqrt{3} \) + 2\( \sqrt{3} \)

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