The equation for this sequence is:

a_n = a_n-1 + 9

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 + 9
a₆ = 37 + 9
a₆ = 46

If a single cook can bake 3 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 3 x 2 = 6 large cakes during that time. 37 large cakes are needed for the party so \( \frac{37}{6} \) = 6\(\frac{1}{6}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 19 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 19 x 2 = 38 small cakes during that time. 320 small cakes are needed for the party so \( \frac{320}{38} \) = 8\(\frac{8}{19}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 7 + 9 = 16 cooks.

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.

To simplify this fraction, first find the greatest common factor between them. The factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24] and the factors of 76 are [1, 2, 4, 19, 38, 76]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{24}{76} \) = \( \frac{\frac{24}{4}}{\frac{76}{4}} \) = \( \frac{6}{19} \)

The greatest common factor (GCF) is the greatest factor that divides two integers.