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

## Numbers and Operations

### 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:

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