Intermediate Algebra (11th edition)

OBJECTIVE 2 Find the general term of a sequence.Sometimes we need to

find a general term to fit the first few terms of a given sequence.

Finding the General Term of a Sequence

Determine an expression for the general term of the sequence.

Notice that the terms are all multiples of 5. The firstterm is the secondis

and so on. The general term

will produce the given first five terms. NOW TRY

an= 5 n

5122 ,

5112 ,

5, 10, 15, 20, 25,Á

an

EXAMPLE 2

SECTION 12.1 Sequences and Series 679

The first five terms of

the sequence an = 2n

40

–2

–2 6

The first five terms of an = 2n are graphed

here. The display indicates that the fourth

term is 16; that is, a 4 = 2^4 = 16.

(a) (b)

FIGURE 1

CAUTION Remember that when determining a general term, as in Example 2,

there may be more than one way to express it.

OBJECTIVE 3 Use sequences to solve applied problems.Practical problems

may involve finite sequences.

Using a Sequence in an Application

Saad Alarachi borrows $5000 and agrees to pay $500 monthly, plus interest of 1% on

the unpaid balance from the beginning of the first month. Find the payments for the

first four months and the remaining debt at the end of that period.

The payments and remaining balances are calculated as follows.

First month Payment:

Balance:

Second month Payment:

Balance:

Third month Payment:

Balance:

Fourth month Payment:

Balance:

The payments for the first four months are

$550, $545, $540, $535

and the remaining debt at the end of the period is $3000. NOW TRY

$5000- 4 #$500=$3000

$500+0.01 1 $3500 2 =$535

$5000- 3 #$500=$3500

$500+0.01 1 $4000 2 =$540

$5000- 2 #$500=$4000

$500+0.01 1 $4500 2 =$545

$5000- $500=$4500

$500+0.01 1 $5000 2 =$550

EXAMPLE 3

NOW TRY
EXERCISE 2
Find an expression for the gen-
eral term of the sequence.

• 3, 9, -27, 81,Á

an

NOW TRY ANSWERS

2. an= 1 - 32 n

NOW TRY
EXERCISE 3
Chase borrows $8000 and
agrees to pay $400 monthly,
plus interest of 2% on the un-
paid balance from the begin-
ning of the first month. Find
the payments for the first four
months and the remaining
debt at the end of that period.

3. payments: $560, $552, $544,
   $536; balance: $6400