Intermediate Algebra (11th edition)

(c)

Square, and then multiply. Add. NOW TRY

OBJECTIVE 5 Write a series with summation notation.In Example 4,we

started with summation notation and wrote each series using signs. Given a series,

we can write it with summation notation by observing a pattern in the terms and writ-

ing the general term accordingly.

Writing Series with Summation Notation

Write each sum with summation notation.

(a)

First, find a general term that will give these four terms for and

respectively. Each term is one less than a multiple of 3, so try as the general

term.

(Remember, there may be other expressions that also work.) Since iranges from 1 to 4,

(b)

These numbers are the cubes of 2, 3, 4, 5, and 6, so the general term is

NOW TRY

OBJECTIVE 6 Find the arithmetic mean (average) of a group of numbers.

8 + 27 + 64 + 125 + 216 = a

6

i= 2

i^3

i^3.

8 + 27 + 64 + 125 + 216

2 + 5 + 8 + 11 = a

4

i= 1

13 i- 12.

3142 - 1 = 11 i= 4

3132 - 1 = 8 i= 3

3122 - 1 = 5 i= 2

3112 - 1 = 2 i= 1

3 i- 1

an a 1 ,a 2 ,a 3 , a 4 ,

2 + 5 + 8 + 11

EXAMPLE 5

+

= 405

= 27 + 48 + 75 + 108 + 147

= 31322 + 31422 + 31522 + 31622 + 31722 i=3, 4, 5, 6, 7

a

7

i= 3

3 i^2

SECTION 12.1 Sequences and Series 681

Arithmetic Mean or Average

The arithmetic mean,or average,of a group of numbers is symbolized and is

found by dividing their sum by the number of numbers. That is,

The values of represent the individual numbers in the group, and nrepresents

the number of numbers.

xi

x

a

n

i 1

xi

n

.

x

NOW TRY
EXERCISE 4
Write out the terms and evalu-
ate the series.

a

5