14.1 Arithmetic Sequences

OBJ: • Find terms of

arithmetic sequences

Arithmetic progressions or sequences (A.P.) have a common difference d between each term.

To find d, take any term minus the term before it.

EX: For each progression that is an A.P., find the common difference d. Give a reason

for each answer. 3,3+25, 3+45,… Answer

3+25 – 3 =

25

A.P.

Reason

d = 25

3+25 + 25 =

3+45

EX: For each progression that is an A.P., find the common difference d. Give a reason

for each answer. -4.3,-2.8,-1.3, .2,… Answer

.2 – -1.3 =

1.5

A.P.

Reason

d = 1.5

-4.3 + 1.5 =

-2.8

EX: For each progression that is an A.P., find the common difference d. Give a reason

for each answer. 6.2, 4.4, 2.6, 0.8,… Answer

4.4 – 6.2 =

-1.8

A.P.

Reason

d = -1.8

4.4 + -1.8 =

2.6

EX: For each progression that is an A.P., find the common difference d. Give a reason

for each answer. 5, 10, 20, 40, . . . Answer

Not A.P.

Reason

10 – 5 ≠

20 – 10

Write the next three terms of the A.P.: 1, 1, 7, 5, . . .

8 2 8 4 4 – 1

8 8

3

8

10

8

13

8

16

8

(or 2)

19

8

Write the first four terms of the A.P. whose first term a is 7.5 and

common difference d = -3.7.5 – 3

4.5 – 3

1.5 – 3

-1.5

The nth term of an arithmetic progression or sequence is given by the formula: l = a + (n – 1) dFind the 36th term of

14, 10, 6, 2,…

10 – 14 =

-4

14 + 35(-4)

14 – 140

-126

Find the 26th term of

8, 5.4, 2.8, 0.2,…

5.4 – 8 =

-2.6

8 + 25(-2.6) =

8 – 65 =

-57

The nth term of an arithmetic progression or sequence is given by the

formula: l = a + (n – 1) dFind the 31st term of 3-2,1,-1+2,...

-1+2 – 1 =

-2+2 =

3-2 + 30(-2 + 2) =

3-2 – 60 + 302) =

-57 + 292

14.4 Geometric Sequences

OBJ: • Find terms of

geometric sequences

Geometric progressions or sequences (G.P.) have a common ratio r between each term

To find r, take any term divided by the

term before it.

EX: For each progression that is an G.P., find the common ratio r. Give a reason for

each answer. 5, 52, 10, 102,...Answer

52

5

2

G.P.

Reason

r = 2

52 • 2 =

10

EX: For each progression that is an G.P., find the common ratio r. Give a reason for

each answer. -8, 4, -2, 1,…Answer

4

-8

-1

2

Reason

r = -1

2

• -1

2 =

-2

EX: For each progression that is an G.P., find the common ratio r. Give a reason for

each answer. -2, -6, -18, -54,…Answer

-6

-2 =

3

Reason

r = 3-6 • 3

-18

EX: For each progression that is an G.P., find the common ratio r. Give a reason for

each answer. 2, 4, 6, 8, . . .Answer

8 ≠ 6 6 4

Not G.P.

Reason

Is an A.P. (d = 2)

EX: For each progression that is an G.P., find the common ratio r. Give a reason for

each answer. 3, .6, .12, .024, . . .Answer

.6

3 =

.2

Reason

r = .2

.6 • .2 =

.12

Write the next three terms of theG.P.: -1, 1, -1, 1, . . .

27 9 3 1

9_

-1

27

1 • -27

9

-3

1 • -3

-3 • -3

9 • -3

-27

Write the first four terms of the G.P. whose first term a is 0.04 and common ratio r = -10.

.04 • -10

-.4 • -10

4 • -10

-40

The nth term of an geometric progression or sequence is given by the formula: l = a •rn – 1

EX: 7th term:

a = 1 and r = -2

8

1 (-2)6

8

1 (64)

8

8

Find the 10th term of

the G.P.:

1, -1, 2, -4, . . .

2

1 (-2)9

2

1 (-512)

2

-256

The nth term of an geometric progression or sequence is given by the formula: l = a •rn – 1

Find the 10th term of the G. P.:

64, -32, 16, -8, …

64 (-1/2)9

64 • -1_

512

-1_

8