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Dr. Fowler AFM Unit 7-2
Arithmetic Sequences
Video – Sigma Notation:https://www.youtube.com/watch?v=KdD-HhmMcrc
8 minutesPay 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.
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
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
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.
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
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
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
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
Find the sum: 52 + 57 + 62 + 67 + … + 122
122 52 51n
70 1 5n
14 1n
15 n
15
1552 122
2S
1305
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
Excellent Job !!!Well Done
Stop NotesDo Worksheet
Sum of Sequence on the Graphing Calculator:https://www.youtube.com/watch?v=N4l2xJgESd4
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