SAT SUBJECT TEST MATH LEVEL 1

MISCELLANEOUS TOPICS

CHAPTER 18
Sequences

GEOMETRIC SEQUENCES

A geometric sequence is a sequence such as 3, 6, 12, 24, 48, . . . in which the ratio between any two consecutive terms is the same. In this sequence, the ratio is

An easy way to find the nth term of a geometric sequence is to start with the first term and multiply it by the common ratio n – 1 times. Here the 5th term is 48, which can be obtained by taking the first term, 3, and multiplying it by the common ratio, 2, four times: 3 × 2 × 2 × 2 × 2 = 3 × 2⁴ = 3 × 16 = 48. In the same way, the 100th term is 3 × 2⁹⁹.

Key Fact Q3

If a₁, a₂, a₃, . . . is a geometric sequence whose common ratio is r, then a_n = a₁r^n-1.

EXAMPLE 5: What is the 12th term of the sequence 3, –6, 12, –24, 48, –96, . . . ?

This is a geometric sequence whose common ratio is –2. By KEY FACT Q3,

 a₁₂ = a₁(–2)¹¹ = 3(–2)¹¹ = 3(–2,048) = –6,144