Post on 31-Dec-2015
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Infinite Sequence: A sequence without bound - -
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, … ? (what’s next 2 terms)
We use the letter, a, with a subscript to represent function values of a sequence.
1, 1, 2, 3, 5, 8….
a1 = 1 a2 = 1 a3 = 2 a4 = 3 a5 = 5 a6 = 8
Finite Sequence: Find the first n terms only.
an represents the nth term of a sequence…. The entire sequence is represented by an
1. Find the first four terms of the sequence given by an = 3n – 2
2. Find the first four terms of the sequence given by: an = 3 + (-1)n
3. Find the first four terms of the sequence given by: an =
[2nd] [Stat] OPS #5[Seq]
Seq (function, variable, first term, last term)
Hit the right arrow key if all values are not visible.
SEQUENCES IN YOUR CALCULATOR
OR…. Change the mode on calculator to seq Plug in equation beside u(n) Graph Use trace to toggle through values
A recursion formula defines the nth term (an) of a sequence as a function of the previous term (an-1)
4. Find the first four terms of the sequence where a1 = 5 and an = 3an-1 + 2, where n>2.
5. Find the first four terms of the sequence where a1 = 3 and an = 2an-1 + 5, where
n>2.
Factorial NotationProducts of consecutive positive integers; the integers decrease by one…..
Example: 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
6. 2 3!∙ 7. (2 3)!∙
n
iia
1
4
1
3i
i
3
0 !
1
j j
Summation Notation
Compact notation for expressing the first n sums of a sequence a1 + a2 + a3 +… an =
11. 12.
[2ND] [Stat] Math #5 [sum]
Then enter sequence… Sum(seq(function, variable, first term, last term))
Summations in your calculator