Intermediate Algebra (11th edition)

Second formula for

Let

Work inside the brackets.

Subtract and then multiply.

NOW TRY

As mentioned earlier, linear expressions of the form where kand care

real numbers, define an arithmetic sequence. For example, the sequences defined by

and are arithmetic sequences. For this reason,

represents the sum of the first nterms of an arithmetic sequence having first term

and general term We can find

this sum with the first formula for as shown in the next example.

Using Snto Evaluate a Summation

Evaluate

This is the sum of the first 12 terms of the arithmetic sequence having

This sum, is found with the first formula for

First formula for

Let.

Evaluate and.

Add.

= 144 Multiply.

= 61242

= 611 + 232 a 1 a 12

S 12 = n= 12

12

2

312112 - 12 + 121122 - 124

Sn= Sn

n

2

1 a 1 + an 2

2 n-1. S 12 , Sn.

an =

a

12

i= 1

12 i- 12.

EXAMPLE 9

Sn,

a 1 = k 112 +c=k+ c an=k 1 n 2 + c= kn+ c.

a

n

i= 1

1 ki+ c 2

an= 2 n+ 5 an=n- 3

kn+ c,

=- 32

= 436 - 144

S 8 = a 1 =3, d=-2, n=8.

8

2

32132 + 18 - 121 - 224

Sn= Sn

n

2

32 a 1 + 1 n- 12 d 4

SECTION 12.2 Arithmetic Sequences 689

NOW TRY
EXERCISE 8
Evaluate the sum of the first
nine terms of the arithmetic
sequence having first term
and common difference - 5.

- 8

NOW TRY ANSWERS
8.- 252 9. 253

NOW TRY

EXERCISE 9

Evaluate a

11

i= 1

15 i- 72.

Complete solution available
on the Video Resources on DVD

If the given sequence is arithmetic, find the common difference d. If the sequence is not arith-

metic, say so. See Example 1.

1. 
   
   
   
   2. 3.2, 6, 10, 4.
      5.10, 5, 0, -5, -10,Á 6.-6, -10, -14, -18,Á
   
   
   
   

- 4, -8, -12,Á 1, 2, 4, 7, 11, 16,Á

1, 2, 3, 4, 5,Á 2, 5, 8, 11,Á

12.2 EXERCISES

a 1 a 12

NOW TRY