SEQUENCES AND SERIES 11.1 NOTES

WARM-UP Describe the pattern below & list the next 3 numbers in the pattern: 1, 1, 2, 3, 5, 8, 13, 21…

SEQUENCES In the most basic sense, we can think of a sequence as a number pattern.

EXAMPLE 1 Since sequences are functions, we could use function notation, but more frequently we do something like this: Write out the first three terms of the sequence.

MORE EXAMPLES Example 2 : Predict the general term for the sequence –1, 1, –1, 1, –1, 1, –1… Example 3: Predict the general term for the sequence 3, 8, 13, 18, 23 …

SERIES If we add up the terms of a sequence, we have a series S 4 means you add up the first four terms of the sequence.

EXAMPLE 4 Find S 6 for the sequence below. 3, 8, 13, 18, 23 … *If you know the general term for a sequence, there is a shorter way to write a series.

SIGMA NOTATION (SUMMATION NOTATION) Example 5:

LAST EXAMPLE Can you find the general term of the Fibonacci sequence? 1, 1, 2, 3, 5, 8, 13, 21…

11.1 HW On mathxlforschool.com due Sunday at midnight.