Algebra 1 Common Core Student Edition, Grade 8-9

Got It? 5. For each recursive formula, find an explicit form ula th a t represents the

same sequence.

a. A( n) = A{ n - 1) + 2; A ( l ) = 21

b. A[ n) = A{ n - 1) + 7; >1(1) = 2

Pr o b l em 6 Writing a Recursive Formula From an Explicit Formula

An arithmetic sequence is represented by the explicit formula A{n) = 32 + (n — 1)(22).

What is the recursive formula?

32 is the firs t term.

A(ri) 32 + (/z 1)(22) - ; 22 is the common difference.

A recursive form ula relates th e value of th e term to th e previous term using the com m on

difference. Use A{ri) to rep resen t th e value of th e term a n d A(n - 1) to re p resen t th e value of the

previous term.

The arithm etic sequence is re p resen te d by th e recursive form ula A{ri) = A {n - 1) + 22;

A (l) = 32.

^ Got It? 6. For each explicit form ula, find a recursive form ula th at rep resen ts the

sequence.

a. A{n) = 76 + ( n - 1)(10)

b. A{n) = 1 + (n - 1)(3)

same

Lesso n Ch eck

Do y o u k n o w H OW?

Describe a pattern in each sequence. Then find the next

two terms of the sequence.

1. 3, 11, 19, 2 7 ,...


2. 3, - 6 , 12, - 2 4 ,...

Tell whether the sequence is arithmetic. If it is, identify

the common difference.

3. 1, - 7 , -1 4 , - 2 1 ,...


4. 1 1 ,2 0 ,2 9 ,3 8 ,...


5. Write a recursive an d an explicit form ula for the
   arithm etic sequence.

9, 7,5,3,1,...

MATHEMATICAL

Do y o u UN DERSTAN D? PRACTICES

6. V o c a b u l a r y C onsider th e following arithm etic

sequence: 25,19,13, 7 ,... Is th e co m m o n difference

6 or - 6? Explain.

7. Error Analysis D escribe an d correct th e error below
   in finding th e te n th term of th e arithm etic sequence
   4,12, 20, 28,...

@ 8. R e a s o n i n g Can you use th e explicit form ula below

to find th e nth term of an arithm etic sequence w ith a

first term A (l) an d a co m m o n difference d? Explain.

A{ri) = A (l) + n d - d

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