## SAT SUBJECT TEST MATH LEVEL 2

## PART 2

## REVIEW OF MAJOR TOPICS

## CHAPTER 3

## Numbers and Operations

3.4 Sequences and Series

### SERIES

In a geometric sequence, if |*r*| < 1, the sum of the series approaches a limit as *n* approaches infinity. In the formula the term Therefore, as long as , or

**EXAMPLES**

**1. Evaluate (A)** and

**(B)**

Both problems ask the same question: Find the sum of an infinite geometric series.

**(A)** When the first few terms, , are listed, it can be seen that and the common ratio . Therefore,

**(B)** When the first few terms, , are listed, it can be seen that *t*_{1 }= 1 and the common ratio . Therefore,

**2. Find the exact value of the repeating decimal 0.4545 . . . .**

This can be represented by a geometric series, 0.45 + 0.0045 + 0.000045 + · · · , with *t*_{1 }= 0.45 and *r* = 0.01.

Since ,

**3. Given the sequence 2, x , y , 9. If the first three terms form an arithmetic sequence and the last three terms form a geometric sequence, find x and y .**

From the arithmetic sequence, , substitute to eliminate *d*.

From the geometric sequence , substitute to eliminate *r.*

Use the two equations with the * to eliminate *y* :

Thus, or 4.

Substitute in *y* = 2*x* – 2: