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Arithmetic Sequences Sequence is a list of numbers typically with a pattern.

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.

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Arithmetic Sequences Sequence is a list of numbers typically with a pattern.






Presentation on theme: "Arithmetic Sequences Sequence is a list of numbers typically with a pattern."— Presentation transcript:

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