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Dr. Fowler AFM Unit 7-2 Arithmetic Sequences

Dr. Fowler AFM Unit 7-2 Arithmetic Sequences. Video – Sigma Notation: 8 minutes Pay close attention!!

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Page 1: Dr. Fowler AFM Unit 7-2 Arithmetic Sequences. Video – Sigma Notation:  8 minutes Pay close attention!!

Dr. Fowler AFM Unit 7-2

Arithmetic Sequences

Page 2: Dr. Fowler AFM Unit 7-2 Arithmetic Sequences. Video – Sigma Notation:  8 minutes Pay close attention!!
Page 3: Dr. Fowler AFM Unit 7-2 Arithmetic Sequences. Video – Sigma Notation:  8 minutes Pay close attention!!

Video – Sigma Notation:https://www.youtube.com/watch?v=KdD-HhmMcrc

8 minutesPay close attention!!

Page 4: Dr. Fowler AFM Unit 7-2 Arithmetic Sequences. Video – Sigma Notation:  8 minutes Pay close attention!!

An An Arithmetic SequenceArithmetic Sequence is is defineddefined as a sequence in as a sequence in which there is a which there is a common common

differencedifference between between consecutive terms.consecutive terms.

Page 5: Dr. Fowler AFM Unit 7-2 Arithmetic Sequences. Video – Sigma Notation:  8 minutes Pay close attention!!

Are the following sequences are arithmetic?If Yes, identify the common difference.

3, 1, 1, 3, 5, 7, 9, . . .

15.5, 14, 12.5, 11, 9.5, 8, . . .

84, 80, 74, 66, 56, 44, . . .

8, 6, 4, 2, 0, . . .

50, 44, 38, 32, 26, . . .

YES 2d

YES

YES

NO

NO

1.5d

6d

Page 6: Dr. Fowler AFM Unit 7-2 Arithmetic Sequences. Video – Sigma Notation:  8 minutes Pay close attention!!

The general form of an ARITHMETIC sequence.

1aFirst Term:

Second Term: 2 1a a d

Third Term:

Fourth Term:

Fifth Term:

3 1 2a a d

4 1 3a a d

5 1 4a a d

nth Term: 1 1na a n d

Page 7: Dr. Fowler AFM Unit 7-2 Arithmetic Sequences. Video – Sigma Notation:  8 minutes Pay close attention!!

Formula for the nth term of an ARITHMETIC sequence.

1 1na a n d

The nth termna

The term numbern

The common differenced

1 The 1st terma

If we know any

If we know any three of these we

three of these we ought to be able

ought to be able to find the fourth.

to find the fourth.

Page 8: Dr. Fowler AFM Unit 7-2 Arithmetic Sequences. Video – Sigma Notation:  8 minutes Pay close attention!!

Given: 79, 75, 71, 67, 63, . . .Find: 32a

1 79

4

32

a

d

n

1

32

32

1

79 32 1 4

45

na a n d

a

a

IDENTIFY SOLVE

Page 9: Dr. Fowler AFM Unit 7-2 Arithmetic Sequences. Video – Sigma Notation:  8 minutes Pay close attention!!

Find the sum of the terms of this arithmetic series.

35

1

29 3k

k

1

2nn a a

S

1

35

35

26

76

n

a

a

35 26 76

2875

S

S

Page 10: Dr. Fowler AFM Unit 7-2 Arithmetic Sequences. Video – Sigma Notation:  8 minutes Pay close attention!!

Find the sum of this series 36

0

2.25 0.75j

j

2.25 3 3.73 4.5 . . .

12 1

2

n a n dS

It is not convenient to It is not convenient to find the last term.find the last term.

1

37

2.25

0.75

n

a

d

37 2 2.25 37 1 0.75

2582.75

S

S

Page 11: Dr. Fowler AFM Unit 7-2 Arithmetic Sequences. Video – Sigma Notation:  8 minutes Pay close attention!!

Find the twenty fourth term of the arithmetic sequence:

–3, 0, 3, 6, . . .

1 3 3a d 3 1 3na n

24 3 24 1 3 66a

Page 12: Dr. Fowler AFM Unit 7-2 Arithmetic Sequences. Video – Sigma Notation:  8 minutes Pay close attention!!

Find the sum: 52 + 57 + 62 + 67 + … + 122

122 52 51n

70 1 5n

14 1n

15 n

15

1552 122

2S

1305

Page 13: Dr. Fowler AFM Unit 7-2 Arithmetic Sequences. Video – Sigma Notation:  8 minutes Pay close attention!!

35

1

45 5i

i

1

2nn a a

S

12 1

2

n a n dS

135 40 130nn a a 135 40 5n a d

35 40 130

21575

S

S

35 2 40 35 1 3

21575

S

S

Page 14: Dr. Fowler AFM Unit 7-2 Arithmetic Sequences. Video – Sigma Notation:  8 minutes Pay close attention!!

Excellent Job !!!Well Done

Page 15: Dr. Fowler AFM Unit 7-2 Arithmetic Sequences. Video – Sigma Notation:  8 minutes Pay close attention!!

Stop NotesDo Worksheet

Page 16: Dr. Fowler AFM Unit 7-2 Arithmetic Sequences. Video – Sigma Notation:  8 minutes Pay close attention!!

Sum of Sequence on the Graphing Calculator:https://www.youtube.com/watch?v=N4l2xJgESd4