Algebra 1 Common Core Student Edition, Grade 8-9

i) Writing an Explicit Formula

Online Auction An online auction works as shown below. Write an explicit formula

to represent the bids as an arithmetic sequence. What is the twelfth bid?

Minimum Price: $200

Bid 1: $200

Bid 2: $210

Bid 3: $220

Bid 4: $230

Rr st Bi d : Th e sel l er set s a

minimum price, which must

be met by the first bid.

Fo l l o w i n g Bi d s: Bi d s i n cr ease

in regular increments.

Make a table of the bids. Identify th e first term a n d co m m o n difference.

What information do
you need to w rite a
rule fo r an arithm etic
sequence?
You need the first term
o f the sequence and the
common difference.

1 234

200 210 220 230

The first term

A( 1) is 2 00.

+ 10 +10 +10 The com m on

difference d is 10.

S ubstitute A (l) = 200 a n d d = 10 into th e form ula A(n) = A (l) + (n — \)d. The explicit

formula A[n) - 200 + (n - 1)10 rep resen ts th e arithm etic seq u e n ce of th e auction bids.

To find th e twelfth bid, evaluate A(n) for n = 12.

A(12) = 200 + (12 - 1)10 = 310

The twelfth bid is $310.

ty Got It? 4. a. A subway pass has a starting value of $ 100. After one ride, the value of the

pass is $98.25. After two rides, its value is $96.50. After three rides, its value

is $94.75. Write an explicit form ula to represent the rem aining value on the

card as an arithm etic sequence. W hat is the value of the pass after 15 rides?

b. Reasoning How m any rides can b e tak en w ith th e $100 pass?

You can write an explicit form ula from a recursive form ula an d vice versa.

Writing an Explicit Formula From a Recursive Formula

An arithmetic sequence is represented by the recursive formula A{n) = A{n - 1) + 12.

If the first term of the sequence is 19, write the explicit formula.

Adding 12 to the previous

term means that the common

difference d is 12

The first term is 19, so A (l) = 19.

A (n ) = A{n — 1) + 12

A{n) = A (l) + (n - 1 )d General form of an explicit formula

A{ri) - 19 + [n - 1)12 Substitute 19 fo r A (1 ) and 12 fo r d.

The explicit formula A{n) = 1 9 + (n - 1)12 rep resen ts th e arithm etic sequence.

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