Algebra 1 Common Core Student Edition, Grade 8-9

Arithmetic Sequences

Co m m o n Co r e St at e St a n d a r d s

F-IF.A.3 Reco g n i ze t h at seq u en ces ar e f u n ct i o n s,

so m et i m es d ef i n ed r ecu r si v e l y ,... Also A-SSE.A.1a,

F-BF.A.1a, F-BF.A.2, F-LE.A.2

M P 1, M P 2, M P 3, M P 4, M P 7

Objectives To identify an d extend p attern s in sequences

To represent arithm etic sequences using function n otation

Getting Ready! «► X C

Id e n tify the

pattern so you can

extend it.

MATHEMATICAL

PRACTICES

A wooden p o st - an d - r ai l f en ce w it h t w o r ai l s is m ade as show n below.

Fi n d t h e n u m b er o f p i eces o f wood n eed ed t o b u i l d a 4 - se c t i o n f e n c e ,

a 5- sect io n f en ce, and a 6 - sect i o n f en ce. Su p p o se you w ant t o build a

fence with 3 rails. How many pieces of wood are needed for each size

fence? Describe the pattern.

7 «v

4 pieces 7 pieces

I..... j

J

ST....7T-

10 pieces

Lesso n \

Vocabulary

sequence

te rm o f a

sequence

• arithm etic
  sequence


• common
  difference


• recursive form ula


• explicit form ula

Pi q n ____

How can you identify

a pa tte rn?

Look at how each term

o f the sequence is related

to the previous term.

Your goal is to identify a

single rule tha t you can

apply to every term to

produce the next term.

In the Solve It, the num b ers of pieces of w ood used for 1 section of fence, 2 sections of

fence, an d so on, form a pattern, or a sequence. A sequence is an o rdered list of num bers

th at often form a pattern. Each n u m b er in the list is called a term of a sequence.

Essent ial Und er st and ing W hen you can identify a p attern in a sequence, you

can use it to extend th e sequence. You can also m odel som e sequences w ith a function

rule th at you can use to find any term of th e sequence.

Extending Sequences

Describe a pattern in each sequence. What are the next two terms

of each sequence?

Q 5, 8, 11, 1 4 ,... 0 2.5,

A p attern is "add 3 to th e previous

term." So th e next two term s are

14 + 3 = 17 a n d 17 + 3 = 20.

A p attern is "m ultiply the previous

term by 2." So th e next two term s are

2(20) = 40 an d 2(40) = 80.

2 7 4 Chap t er 4 An Int ro d uct io n t o Funct ions

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