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 multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

9c⁶ x 8c⁷
(9 x 8)c^{(6 + 7)}
72c¹³

You have 40 out of the total of 450 raffle tickets sold so you have a (\( \frac{40}{450} \)) x 100 = \( \frac{40 \times 100}{450} \) = \( \frac{4000}{450} \) = 9% chance to win the raffle.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [40, 80] making 40 the smallest multiple 8 and 10 share.

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

\( \frac{8 x 5}{8 x 5} \) + \( \frac{4 x 4}{10 x 4} \)

\( \frac{40}{40} \) + \( \frac{16}{40} \)

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

\( \frac{40 + 16}{40} \) = \( \frac{56}{40} \) = 1\(\frac{2}{5}\)

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.