1.) Use the fact that , to evaluate .

 For #2 through #4 use the following arithmetic or geometric sequences:

{a_n} = -3200, 2400, -1800, 1350, ...
{b_n} = 35, 40, 45, 50, 55, ...
{c_n} = 12, 18, 27, ...

2.) Find the recursive formula for each of the above.

3.) Find the explicit formula for each of the above.

4.) Evaluate each of the following if it exists.

5.) Write the following rational number as a reduced fraction:

6.) For each expression on the left put the letter of the expression on the right that is equivalent to it. Some answers will be used more than once.

(i) _____        (iii) ____    (v) _____ (vii) ____

(ii) ____   (iv) ____ (vi) ____ (viii) ____

1 n

7.) Expand and simplify each of the following:

1. (3x – 2y)⁴                                      b.

 

9.) Find the term containing the factor x ³, of the expansion of

10) Find the first three terms of the following explicitly defined sequence.

 11.) Find the first five terms of the following recursively defined sequence.

for

12.) Suppose is an arithmetic sequence where a₅ = -9 and a₁₂ = -65 . Find a₂₀ .

13.) A ball is dropped from a height of 480 feet. It rebounds 1/4 the distance of the previous fall after each bounce.

(a.) How far has the ball traveled by the time it hits the ground for the third time.

(b.) What is the total distance the ball travels?

14.) Evaluate the following sums (assume c is a constant) :

a. 

b. (Write in terms of c without the summation.)

c.

 

15.) Let a₁ be the first term of the following sequence: 7, 17, 27, 37, … . Evaluate a₄ and a₂₀₀ .

16.) A college planning committee consists of 3 freshmen, 4 sophomores, 5 juniors, and 2 seniors. A subcommittee of 4 consisting of 1 individual from each class is to be chosen. How many different subcommittees are possible?

17.) From a group of 5 men and 7 women, how many different committees consisting of 2 men and 3 women can be formed?

18.) How many ways can 4 couples (husbands and wives) sit in eight seats in a row at a baseball game if all the women sit next to each other?

19.) A child has 12 blocks, of which 6 are black, 4 are red, 1 is white, and 1 is blue. If the child puts the blocks in a line, how many distinguishable arrangements are possible?

20.) If 4 Americans, 3 Frenchman, and 3 Englishmen are to be seated in a row, how many seating arrangements are possible when people of the same nationality must sit next to each other?

21.) A family with 13 people needs to clean up their yard before the winter snow hits. However, sometimes not everyone is available to help with the yard work due to other responsibilities (a lot of homework, and employment). If at least one member of the family must work on the yard today, how many possible combinations of family members will work in the yard today?

answers:

1.) 121486

2.)

3.)

4.)
   

5.)     6.) (i.) d (ii.) e (iii.) a (iv.) f (v.) g (vi.) c (vii.) g (viii.) f