1. Find n when a₁= 45, d = 9, and a_n= 81.

2. Expand (2x=5y)⁶

^{What is the expansion?}

3. From the 12 male and 9 female sales representatives for an insurance company, a team of 3 men and 4 women will be selected to attend a national conference on insurance fraud.

- In how many ways can the team of 7 be selected?

4. How many 4 - digit numbers can be formed using the digits 2,3,4, and 6 without repetition? With repetition?

- A total of ___ different 4 - digit numbers can be formed using the digits 2,3,4, and 6 without repetition.

- A total of ___ different 4 - digit numbers can be formed using the digits 2,3,4, and 6 with repetition.

5. Find the sum, if it exists.

75+45+27+ ...

6. Determine the nth term of the geometric sequence.

1,4,16,64, ...

7. A theater has 24 rows of seats. The first row has 18 seats, the second row has 20 seats, the third row has 22 seats, and so on. How many seats are in the theater?

8. Suppose we select, without looking, one marble from a bag containing 3 red marbles and 11 green marbles. What is the probability of selecting each of the following?

a) A red marble b) A green marble

c) A purple marble d) A red or a green marble

9. Rewrite the sum using sigma notation.

1/1*4 + 1/2*5 + 1/3*6 + 1/4*7 + ...