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 Download Presentation

Lesson 3.13 Applications of Arithmetic Sequences Concept: Arithmetic Sequences EQ: How do we use arithmetic sequences to solve real world problems? F.LE.2 Vocabulary: Arithmetic sequence, Common difference

4. 3. 2. 1. 0. In addition to level 3.0 and above and beyond what was taught in class, the student may:. · Make connection with other concepts in math. · Make connection with other content areas..

by k . woodard. and k . norman. Arithmetic Sequence. Add or Subtract. . . the . same number . each time. This is called the . common difference. examples. 2, 4, 6, 8, …. . common difference is 2.

Goals and Objectives. Students will be able to understand how the common difference leads to the next term of an arithmetic sequence, the explicit form for an Arithmetic sequence, and how to use the explicit formula to find missing data..

Arithmetic Sequences. An arithmetic sequence is a sequence in which each term after the first differs from the preceding term by a constant amount.. The difference between consecutive terms is called the .

Section 8.2 beginning on page 417. Identifying Arithmetic Sequences. In an . arithmetic sequence. , the difference of consecutive terms is constant. This constant difference Is called . common difference.

An introduction…………. Arithmetic Sequences. ADD. To get next term. Geometric Sequences. MULTIPLY. To get next term. Arithmetic Series. Sum of Terms. Geometric Series. Sum of Terms. Find the next four terms of –9, -2, 5, ….

By: Matt Connor. Fall 2013. Pure Math. Analysis. Calculus and Real Analysis . Sequences. Sequence- A list of numbers or objects in a specific order. 1,3,5,7,9,...... Finite Sequence- contains a finite number of terms.

th. term, directly. Today you will investigate recursive sequences. A term in a recursive sequence depends on the term(s) before it.. 5-71.. Look at the following sequence: . –8, –2, 4, 10, ….

Formulas booklet page 3. In maths, we call a list of numbers in order a . sequence. .. Each number in a sequence is called a . term. .. 4, 8, 12, 16, 20, 24, 28, 32, . . .. 1. st. term. 6. th. term.

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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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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

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