Algebra 1 Common Core Student Edition, Grade 8-9

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How can you identify
an arithm etic
sequence?
The difference between
every pair o f consecutive
terms must be the same.

Go t I t? 1. D escribe a p a ttern in each sequence. W hat are th e next two term s of each

sequence?

a. 5 ,1 1 , 17, 2 3 ,... b. 400, 200, 100, 50,...

C. 2 , - 4 , 8 , - 1 6 ,... d. - 1 5 , - 1 1 , - 7 , - 3 ,...

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In an arithmetic sequence, the difference b etw een consecutive term s is constant. This

difference is called th e common difference.

Id en tifyin g a n A rithm etic Sequence

Tell whether the sequence is arithmetic. If it is, what is the com m on difference?

Q3, 8, 13, 18,... Q6, 9, 13, 17,...

+5 +5 +5 +3 +4 +4

The seq u en ce has a co m m o n difference

of 5, so it is arithm etic.

The seq u en ce does n o t have a com m on

difference, so it is n o t arithm etic.

0G o»H? 2. Tell w h e th e r th e seq u en ce is arithm etic. If it is, w hat is th e com m on

difference?

a. 8,15,22, 30,...

c. 10 ,4 , - 2 , - 8 ,..

b. 7,9,11, 13,...

d. 2 , - 2 , 2 , -2, ...

A sequence is a function w hose d o m ain is th e n atu ral num bers, an d w hose outputs are

th e term s of th e sequence.

You can w rite a seq u en ce using a recursive form ula. A recursive fo rm u la is a function

rule th a t relates each term of a seq u e n ce after th e first to th e ones before it. C onsider

th e seq u en ce 7 , 1 1 , 1 5 , 1 9 ,... You can use th e co m m o n difference of th e term s of an

arithm etic sequence to w rite a recursive form ula for th e sequence. For th e sequence

7 , 1 1 , 1 5 , 1 9 ,... , the c o m m o n difference is 4.

Let n = the term n u m b e r in th e sequence.

Let A{ri) = th e value of th e n th term of th e sequence.

value of term 1 = A (l) = 7

value of term 2 = A(2) = A (l) + 4

value of term 3 = A(3) = A(2) + 4 = 15

value of term 4 = A(4) = A(3) + 4 = 19

value of term n = A{ri) = A {n - 1) + 4

The recursive form ula for th e arith m etic seq u e n ce above is A[n) = A(n — 1) + 4,

where A(l) = 7.

The value o f th e previous

te rm plus 4

The common difference is 4.

PowerAlgebra.com Lesso n 4- 7 A r i t h m e t i c Seq u en ces 275