SAT SUBJECT TEST MATH LEVEL 2

PART 2

REVIEW OF MAJOR TOPICS

CHAPTER 3

Numbers and Operations


3.4 Sequences and Series

EXERCISES

1. If a= 3 and a= n + an–1, the sum of the first five terms is

      (A)  17

      (B)  30

      (C)  42

      (D)  45

      (E)  68

2. If a= 5 and  find a3.

      (A)  2.623

      (B)  2.635

      (C)  2.673

      (D)  2.799

      (E)  3.323

3. If the repeating decimal  is written as a fraction in lowest terms, the sum of the numerator and denominator is

      (A)  16

      (B)  47

      (C)  245

      (D)  334

      (E)  1237

4. The first three terms of a geometric sequence are  The fourth term is

      (A)  

      (B)  

      (C)  

      (D)  

      (E)  

5. By how much does the arithmetic mean between 1 and 25 exceed the positive geometric mean between 1 and 25?

      (A)  5

      (B)  about 7.1

      (C)  8

      (D)  12.9

      (E)  18

6. In a geometric series  and . What is r ?

      (A)  

      (B)  

      (C)  

      (D)  

      (E)  

Answers and Explanations

1. (D) a2 = 5, a3 = 8, a4 = 12, a5 = 17. Therefore, S5 = 45

2. * (D) Press 5 ENTER into your graphing calculator. Then enter  and press ENTER twice more to get a3.

3. * (C) The decimal  = 0.2 + (0.037 + 0.00037 + 0.0000037 + · · ·), which is 0.2 + an infinite geometric series with a common ratio of 0.01.

            The sum of the numerator and the denominator is 245.

4. (D) Terms are 31/4, 31/8, 1. Common ratio = 3–1/8. Therefore, the fourth term is 1 · 3–1/8 = 3–1/8 or 

5. (C) Arithmetic mean  Geometric mean  The difference is 8.

(D)  Therefore,