Algebra 1 Common Core Student Edition, Grade 8-9

Which term number

represents th e 6th

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The 1 st term represents

the original price, the

2nd term represents

the 1st markdown, the

3rd term represents the

2nd markdown, and so

on. Therefore, the 7th

term represents the 6th

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Think
W h a t is th e d o m a in o f
the sequence? W hat
is th e d o m a in o f th e
function?
The domain of the
sequence is positive
integers > 1. The domain
of the function is ail real
numbers.

Two managers at a clothing store created sequences to show the original price

and the marked-down prices of an item. Write a recursive formula and an

explicit formula for each sequence. What will the price of the item be after the 6th

markdown?

Using Sequences

First Sequence

$60, $51, $43.35, $ 3 6 .8 5 ,...

com m on ratio = 0.85

ax = 60

Cl y, an-1 0.85

= 60 • 0.85” “ 1

a7 = 60 • 0.857-1

Recursive formula

Explicit formula

Second Sequence

$60, $52, $44, $ 3 6 , ...

common difference = —8

ax = 60

an ~ an-1 — 8

an = -8(n - 1) + 60

Substitute 7 for n.

a7 ~ $22.63 Simplify.

The price continuing th e first seq u e n ce is $22.63 after th e 6th m arkdow n.

The price continuing th e seco n d seq u en ce is $12 after th e 6th m arkdow n.

a7 = - 8 ( 7 - 1) + 60

a7 = $12

& Got It? 3. W rite a recursive form ula an d an explicit form ula for each sequence. Find

th e 8th term of each sequence.

a. 14, 84, 504, 3 0 2 4 ,... b. 648, 324, 162, 8 1 ,...

You can also rep resen t a seq u e n ce by using function notation. This allows you to plot

th e seq u en ce using th e points (n, an), w here n is th e term n u m b e r a n d an is th e term.

Pr o b l em 4 Writ ing Geomet ric Sequences as Funct ions

A geom etric sequence h as a n initial value of 6 an d a co m m o n ratio of 2. W rite a function to

rep resen t the sequence. G raph th e function.

an = ai • r " - 1 Explicit formula

/(x) = 6 • 2X~ 1 Substitute f(x) for an, 6 for a 1 , and 2 for r.

The function f(x) = 6 • 2x ~ l rep resen ts th e geom etric

sequence.

D eterm ine th e first few term s of th e seq u e n ce by using th e function.

/ ( 2 ) = 6 • 22-1 = 12 / ( 4 ) = 6 • 24 “ 1 = 48

/ ( 3 ) = 6 • 23-1 = 24 / ( 5 ) = 6 • 25-1 = 96

Plot th e points (1, 6), (2,12), (3, 24), (4, 48), an d (5, 96).

G ot It? 4. A geom etric seq u e n ce has a n initial value of 2 an d a

co m m o n ratio of 3. W rite a function to re p resen t the

sequence. G raph th e function.

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PowerAlgebra.com Lesso n 7-8 Geo m et r i c Seq uen ces 469