2 4 6 8 The first term in a sequence is denoted as a 1 the second term is a 2 and so on up to the nth term a n Each number in the list called a term a 1 a ID: 729604
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Slide1
Arithmetic SequencesSequence is a list of numbers typically with a pattern.2, 4, 6, 8, …The first term in a sequence is denoted as a1, the second term is a2, and so on up to the nth term an.
Each number in the list called a
term
.
a
1
, a
2
, a
3
, a
4
, …Slide2
Finite Sequence has a fixed number of terms. {2, 4, 6, 8} A sequence that has infinitely many terms is called an infinite sequence. {2, 4, 6, 8,…} Algebraically, a sequence can be written as an explicit formula or as a recursive formula.
Explicit formulas show how to find a specific term number (n).
Recursive formula show how to get from a given term (an-1) to the next term (a
n)Slide3
An Arithmetic Sequence is a sequence where you use repeated addition (with same number) to get from one term to the next.Ex: 4, 1, -2, -5, … is an arithmetic sequence -3 -3 -3
The number that needs to be added each time to get to the next term is called the
common differenceThe common difference for the above arithmetic sequence is
-3 .Slide4
Explicit formula for Arithmetic Sequence: an = + (n - 1)d
Recursive formula for an Arithmetic Sequence:
a1 = #
an = a
n-1 + d
Commondifference
Explicit Formula
Substitute
the values:
a
n
=
4 + (n – 1)(- 3)
So the explicit formula is:
a
n
= -3n + 7
The Recursive Formula is:
a1 = 4 an = an-1 – 3
For the example:
4, 1, -2, -5, …
First termSlide5
A series is the sum of ALL the terms of a sequence. (can be finite or infinite)A partial sum is the sum of the first n terms of a series…denoted Sn
Number of terms
First term
Last term
How do you add these sequences of numbers?Slide6
For the example: 4, 1, -2, -5, …1) Find S4.Find S20. (Think….) Slide7
Example: For the arithmetic sequence 2, 6, 10, 14, 18, …Write the explicit formula for the sequence.Write the recursive formula for the sequence.c) Find the 15th partial sum of the sequence (S15). an =
a
1
= #an
= an-1 + d