Geometric Sequences and Series (Section 8-3)

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Presentation transcript:

Geometric Sequences and Series (Section 8-3)

Geometric Sequence- A sequence in which the ratios of consecutive terms are the same. A sequence is geometric if there is a number r such that r is called the common ratio.

Determine if the sequence is geometric. If it is, find the common ratio. Example 1

Determine if the sequence is geometric. If it is, find the common ratio. Example 2

Determine if the sequence is geometric. If it is, find the common ratio. Example 3

Determine if the sequence is geometric. If it is, find the common ratio. Example 4

Write the first 5 terms of the geometric sequence. Example 5

Write the first 5 terms of the geometric sequence. Example 6

nth term of a geometric sequence:

Find the nth term of the geometric sequence. Example 7

Find the nth term of the geometric sequence. Example 8

Find the formula for the nth term of the geometric sequence Find the formula for the nth term of the geometric sequence. Then find the indicated nth term of the geometric sequence. Example 9 7th term: 3, 36, 432, …

Example 10 The fourth term of a geometric sequence is 125 and the 10th term is . Find the fourteenth term.

Example 11 The second term of a geometric sequence is -18 and the fifth term is . Find the 6th term.

Sum of a FINITE of a geometric sequence:

Find the sum. Example 12

Find the sum. Example 13

Find the sum. Example 14

Use summation notation to write the sum. Example 15 7 + 14 + 28 + …+896

Sum of a INFINITE of a geometric sequence: where

Find the sum of the infinite geometric series, if possible Find the sum of the infinite geometric series, if possible. If not possible, explain why. Example 16

Find the sum of the infinite geometric series, if possible Find the sum of the infinite geometric series, if possible. If not possible, explain why. Example 17

Find the sum of the infinite geometric series, if possible Find the sum of the infinite geometric series, if possible. If not possible, explain why. Example 18

Find the sum of the infinite geometric series, if possible Find the sum of the infinite geometric series, if possible. If not possible, explain why. Example 19

HW #40 pg 607-608 (1, 5, 11, 15, 19, 25-29 odd) HW #41 pg 607-608 (35, 41, 45-53 odd, 59-69 odd) Have both ready to ask questions on Monday. Test Thursday.