Algebra 1 Common Core Student Edition, Grade 8-9

Im ag in e w orking p ar t t im e at a clot hing

st o r e. Each w eek a co at d oesn' t sel l ,

its price is marked down 20%. W hat

will t he sale price f o r t he coat shown

at t h e r i g h t b e a f t e r t h r ee w eek s?

@ Common Core State Standards

F-BF.A.2 Write... geometric sequences both recursively

and w ith an explicit formula, use them to model

situations, and translate between the tw o forms. Also

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

Geo m et ric Seq u en ces

Objective To w rite a n d use recursive form ulas for geom etric sequences

Getting Ready!

What happens as

a n u m b e r g ro w s

or shrinks by the

same fa c to r? T ry

it here, and this

lesson w ill show

you an easier way

to fin d out.

PRACTICES t^ie Solve It, th e sales prices form a geometric sequence.

^ Lesson i
Vocabulary
geometric
sequence

Esse n t i a l U n d e r st a n d i n g In a geom etric sequence, th e ratio of any term to its

preceding term is a co n stan t value.

Key Concept Geometric Sequence

A geom etric seq u en ce w ith a starting value a and a common ratio ris a sequence of the form

a, ar, at2, ai3 ,...

A recursive definition for th e seq u en ce h as two parts:

aY = a Initial condition

an = an_ 1 • r, for n > 2 Recursive formula

An explicit definition for this seq u e n ce is a single form ula:

a„ = a l • rn~ l , for n > 1

Every geom etric seq u en ce h as a starting value an d a c o m m o n ratio. The starting value and

co m m o n ratio define a u n iq u e geom etric sequence.

c

PowerAlgebra.com | Lesso n 7- 8 Geo m et r i £Seq u en ces 467