## 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*_{1 }= 3 and *a _{n }= n + a_{n}*

_{–1}, the sum of the first five terms is

(A) 17

(B) 30

(C) 42

(D) 45

(E) 68

2. If *a*_{1 }= 5 and find *a*_{3}.

(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)** *a*_{2} = 5, *a*_{3} = 8, *a*_{4} = 12, *a*_{5} = 17. Therefore, *S*_{5} = 45

2. * **(D)** Press 5 ENTER into your graphing calculator. Then enter and press ENTER twice more to get *a*_{3}.

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 3^{1/4}, 3^{1/8}, 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.

6 **(D)** Therefore,