LESSON 10-1: SEQUENCES, SERIES, AND SIGMA NOTATION  Investigate several different types of sequences.  Use sigma notation to represent and calculate sums of series.

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sequence term finite & infinite sequences recursive & explicit sequences Fibonacci sequence converge or diverge series, finite series, infinite series nth partial sum sigma notation

Find the next four terms for each of the following sequences. A. 1, 2, 4, 7, 11, 16, 22, …

B. 18, 15, 10, 3, …

C. Find the first four terms of the sequence given by the following explicit formula.

an  2n  1

n

Find the fifth term of the recursively defined sequence.

a1  3, an  3an1  2n  5, where n  2

The Fibonacci sequence describes many patterns found in nature. This sequence is often defined recursively.

a1  1, a2  1, an  an2  an1 , where n  3

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …

Determine whether each sequence is convergent or divergent. Use a graphing calculator, whenever possible.

 1 A. an  4000     4

B. an 

C. an 

 2 

n

n

2

 0.1

n

n

2n  1

D. a1  9, an  an1  4

A. Find the fifth partial sum of an  n2  3.

B. Find the fourth partial sum of an 

6

 2

n

.

C. Find the sixth partial sum of a1  8, an  0.5  an 1  , n  2.

Find each sum. 2 n    n 4

A.

n 1

3i  3 B.  i i 2 5



 1  C.  3   k   10  k 1