Name ____________________________________________________ Date ____________ Algebra 2/Trig: Unit 18 Series and Sequence EXAM DIRECTIONS: Because this is a take home test you must show your work for ALL questions, including multiple choice questions. If you do not need to show your work, please explain how you chose your answer. A correct response on multiple choice with no work shown will not receive credit.

Part I Answer all questions in this part. Each correct answer will receive 1 credit. No partial credit will be allowed. For each question, circle the numeral preceding the word or expression that best completes the statement or answers the question.

1. What is a formula for the nth term of sequence B shown below?

1)

2)

3)

4)

2. What is the common ratio of the geometric sequence whose first term is 27 and fourth term is 64?

1)

2)

3)

4)

3. Which arithmetic sequence has a common difference of 4? (1) {0, 4n, 8n, 12n, . . .} (2) {n, 4n, 16n, 64n, . . .} (3) {n + 1, n + 5, n + 9, n + 13, . . .} (4) {n + 4, n + 16, n + 64, n + 256, . . .}

4. Mrs. Hill asked her students to express the sum using sigma notation. Four

different student answers were given. Which student answer is correct?

(1)

(3)

(2)

(4)

5. Find the sixth term of the geometric sequence for which a1 = 5 and r = 2. (1) 320 (3) 15 (2) 160 (4) 6250

Part II Answer all questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit.

6. Find the first four terms of the recursive sequence defined below.

7. Evaluate: 5

3

1

10 ( 1)n

8. Find the sum of the n terms of the arithmetic series:

10

5.2

5010

n

d

a

9. Find the sum of the geometric series 128 – 64 + 32 - … to 8 terms.

10. The third term of an arithmetic sequence is 15, and the seventh term is 23.

Determine a formula for , the term of this sequence.

11. An arithmetic sequence is given below with terms missing. Part a: Find the first term and the common difference. Part b: Find the sum of the first 36 terms of the arithmetic series above.

12. A geometric sequence is given below with terms missing. Part a: Given two terms in a geometric sequence find the common ratio, and the explicit formula. Part b: Find the sum of the geometric series above if = -9,565,93.8