The equation for this sequence is:

a_n = a_n-1 + 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 + 1
a₆ = 5 + 1
a₆ = 6

You have 6 out of the total of 150 raffle tickets sold so you have a (\( \frac{6}{150} \)) x 100 = \( \frac{6 \times 100}{150} \) = \( \frac{600}{150} \) = 4% chance to win the raffle.

If a single cook can bake 5 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 5 x 3 = 15 large cakes during that time. 24 large cakes are needed for the party so \( \frac{24}{15} \) = 1\(\frac{3}{5}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 20 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 20 x 3 = 60 small cakes during that time. 130 small cakes are needed for the party so \( \frac{130}{60} \) = 2\(\frac{1}{6}\) 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 2 + 3 = 5 cooks.

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{10 + 4 + 10 + 4}{4} \) = \( \frac{28}{4} \) = 7

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:

\( \sqrt{\frac{36}{9}} \)
\( \frac{\sqrt{36}}{\sqrt{9}} \)
\( \frac{\sqrt{6^2}}{\sqrt{3^2}} \)
\( \frac{6}{3} \)
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