4.7 Define & Use 4.7 Define & Use Sequences & SeriesSequences & Series

VocabularyVocabulary A A sequencesequence is a function whose is a function whose

domain is a set of consecutive domain is a set of consecutive integers. If not specified, the integers. If not specified, the domain starts w/ 1. The values domain starts w/ 1. The values in the range are the in the range are the termsterms of the of the sequence. A finite sequence has sequence. A finite sequence has a limited number of terms and a limited number of terms and an infinite sequence continues an infinite sequence continues forever.forever.

When you add the terms of a When you add the terms of a sequence the result is a sequence the result is a seriesseries. . Summation notationSummation notation, or , or sigma sigma notationnotation, is used to write a , is used to write a series. For example, in the series. For example, in the series , i is the index of series , i is the index of

Summation, 1 is the lower limit of Summation, 1 is the lower limit of summation and 4 is the upper summation and 4 is the upper limit of summation.limit of summation.

ExamplesExamples

Write the 1Write the 1stst 6 terms of the 6 terms of the sequence.sequence.

aann = n - 2 = n - 2

Describe the pattern, write the Describe the pattern, write the next term, and write a rule for next term, and write a rule for the nth term of the sequencethe nth term of the sequence

a.a. 3, 6, 9, 12, . . . 3, 6, 9, 12, . . .

b.b. 1/1, 1/3, 1/5, 1/7, . . . 1/1, 1/3, 1/5, 1/7, . . .

Write the series using Write the series using summation notation.summation notation.

a.a. 5 + 6 + 7 + . . . + 125 + 6 + 7 + . . . + 12

b.b. 3 + 5 + 7 + . . . 3 + 5 + 7 + . . .

Find the sum of the series.Find the sum of the series.

4.7 Homework Change4.7 Homework Change

p. 135 1, 2, 8, 10, 18, 19, 22p. 135 1, 2, 8, 10, 18, 19, 22