The equation for this sequence is:

a_n = a_n-1 + 2

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
a₆ = 9 + 2
a₆ = 11

The ratio of football cards to baseball cards is 3:2 and the ratio of baseball cards to basketball cards is 3:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 9:6 and the ratio of baseball cards to basketball cards as 6:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 9:6, 6:2 which reduces to 9:2.

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{48}{12} \) = 4

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

3\( \sqrt{32} \) + 2\( \sqrt{2} \)
3\( \sqrt{16 \times 2} \) + 2\( \sqrt{2} \)
3\( \sqrt{4^2 \times 2} \) + 2\( \sqrt{2} \)
(3)(4)\( \sqrt{2} \) + 2\( \sqrt{2} \)
12\( \sqrt{2} \) + 2\( \sqrt{2} \)

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

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $300
i = 0.04 x $300
i = $12