﻿ ﻿SERIES - Sequences and Series - Numbers and Operations - REVIEW OF MAJOR TOPICS - SAT SUBJECT TEST MATH LEVEL 2

## PART 2 ## REVIEW OF MAJOR TOPICS ## 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 t1 = 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 t1 = 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 = 2x – 2: ﻿