2.  A sequence is a function whose domain is a set of consecutive integers. If a domain is not specified, it is understood that the domain starts with 1. (A list of terms with some pattern)  The values in the range are called the terms of the sequence.  A finite sequence has a limited number of terms.  An infinite sequence continues without stopping.  A sequence can be specified by an equation, or rule.

3.  When the terms of a sequence are added together, the resulting expression is a series.  Summation notation or sigma notation, is used to write a series.  For example, in the series 2i is the index of summation, 1 is the lower limit of summation and 4 is the upper limit of summation.

4.  A factorial is the number and each number smaller than it multiplied together. Its notation is !  For example 5! = 5 * 4 * 3 * 2 * 1 = 120  On the calculator, factorial is found under math, PRB, option 4  (-1) raised to an even power = 1 and (-1) raised to an odd power is -1  For example (-1) 6 = 1 and (-1) 9 = -1

5.  Write the first four terms of these sequences  1.  2.  3. 7, 11,15, 19 1/3, 2/9, 6/27, 24/81 -1, 4, -7, 10

6.  Find the pattern, write a rule for the nth term of the sequence, and then write the next term

7. 12, 15, 18, 21, 24, 27, 30 a n = 3n + 9 Look for a pattern This is going up by 3 each time, this will get multiplied by n, then figure out the 0 th term 12-3 = 9 Pattern 0 th term Next term = 33

8. 34, 27, 20, 13, 6, -1 a n = -7n + 41 Look for a pattern This is going down by 7 each time, this will get multiplied by n, then figure out the 0 th term 34+7 = 41 Pattern 0 th term Next term = -8

9. -5, -1, 3, 7, 11 a n = 4n - 9 Look for a pattern This is going up by 4 each time, this will get multiplied by n, then figure out the 0 th term -5-4=-9 Pattern 0 th term Next term = 15

10. a n = Look for a pattern in the numerator and the denominator separately

11. 1, 4, 9, 16, 25, 36, 49 a n = n 2 Term # 1, 2, 3, 4, 5, 6, 7 What are you doing to the term # (domain) in order to get the term (range)? Squaring it!

12. a n = Nothing is happening to numerator so it will not have n in it

13.  Σ (greek letter sigma) means to add 1 st number to plug into a k Plug in all numbers up until this one Means add Sequence to plug in to It is not important what this letter is

14.  Evaluate 2(3) + 4 + 2(4) + 4 + 2(5) + 4 36

15.  Evaluate 0 + 1 + 4 + 9 + 16 + 25 + 36 91

16.  Evaluate 3/6 + 3/7 + 3/8 73/56

17.  Figure out the pattern and write formula as before  Figure out which numbers are getting plugged in, use these as the beginning and end numbers in sigma notation

18. 1 st number that gets plugged in is 1 (to get 2 in the denominator) last number that gets plugged in is 15 (to get 16 in the denominator)

19. 1 st number that gets plugged in is 1 (to get 1 in the denominator) last number that gets plugged in is 20 (to get 400 in the denominator)

20. Sometimes a series is infinite which means the upper limit is. A partial sum is just the sum of the first few terms of an infinite series. The problem will tell you how many terms to add.

21.  Find the 6 th partial sum of

22.  List math sum(  List ops seq(  Sum(seq(formula, variable, lower limit, upper limit))  Examples:  1.  2.  3.

23.  Set mode to seq  Put sequence in y=  Press graph  You may need to change the viewing window to see enough point  You can also press table (2 nd graph) to see the (x,y) points

24.  Graph the first 6 terms