Section 7.2 Arithmetic Sequences

Arithmetic Sequence

Finding the nth term of an Arithmetic Sequence

Find the next four terms.

13112221

1,11,21,1211,111221,....

312211

1113213211

Find the next four terms.

5,9,13,17,21,...

2925 33

Arithmetic Sequence

a common difference between consecutive terms.

Ex:

Determine if the following are arithmetic

5,9,13,17,21,...

3, 12, 21, 30,...

4x,5x, 7x,10x,...

2 33x,6x ,9x ...

Arithmetic Sequence With a partner find the common difference,

d, for each of the given sequences. You may need to write out the terms if the formula is given.

a)1, 4, 7,10,13,...

b)6,12,18,24,...

c)100,90,80, 70,...

nd)a 4n 3

ne)a 7 5n

n

1f)a n 3

4

3

6

10

4

514

nth term of an arithmetic sequence

n 1a a n 1 d

nth term first term

common difference

Ex: Write out the first five terms of the arithmetic sequence if

1a 10 and d 4

1a 10

2a 14

3a 18

4a 22

5a 26

Ex: From the previous example, find na

n 1a a n 1 d

na 10 n 1 4

na 6 4n

Ex: From the previous example, find 50a

50

50

a 6 4 50

a 206

Ex: Find for the arithmetic sequence having and

18a

18 1a a n 1 d

2a 9 3a 15

1a 3 d 6

18a 3 18 1 6

18a 105

Ex: Find d, and for the arithmetic sequence having and

20a

6a 22 1a

8a 32

6 1a a n 1 d

6a 22

d 5

122 a 6 1 5

1a 3

7a ? 8a 32 7a 27

20 1a a n 1 d

20a 3 20 1 5

20a 92