Lesson 11.4 Geometric Sequences

Warm Up

½

A geometric sequence is a sequence in which the ratio of successive terms is the same number, r, called the common ratio. That is, if is any term in a geometric sequence, the following must be true: The formula for the general term,, is a recursive formula because it gives the nth term of a sequence in relation to the previous term and r. You can also write an explicit formula for the nth term of a sequence by using the first term and r.

A pattern can be seen in the recursive formula for the geometric sequence defined by From the pattern, the explicit formula is

TRY THIS: Find the eight term of the sequence defined by

TRY THIS: Find the 12 th term of a geometric sequence in which n2345 tntn 240??30 rrr

TRY THIS: Find three geometric means between 64 and 4. 64, ?, ?, ?, 4 t5t5 t1t1 32, 16, and 8 OR -32, -16, and -8

Lesson Quiz

Homework Practice 11.4 B