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9.2 Arithmetic Sequence and Partial Sum
Common Difference
Finite Sum
Common Difference
Look at the sequence
3 + 8 + 13 + 18 + ….. To find the common difference
d = an+1 – a1 d = 13 – 8 = 5d = 18 – 13 = 5
d = 5
Rule of Arithmetic Sequence
3 + 8 + 13 + 18 + …..
Find the equation
an = a1 + (n – 1)d
an = 3 + (n – 1)5
an = 3 + 5n – 5
an = -2 + 5n
Find the Rule of Arithmetic Sequence
3 + 10 + 17 + 24 + 31 …….
Find the Rule of Arithmetic Sequence
3 + 10 + 17 + 24 + 31 …….
d = 10 – 3 = 7 d = 17 -10 = 7
Find the Rule of Arithmetic Sequence
3 + 10 + 17 + 24 + 31 …….
d = 10 – 3 = 7 d = 17 -10 = 7
an = 3 + (n – 1)(7)
an = 3 + 7n – 7
an = -4 + 7n
Finite Sum
The equation to find a finite sum
nn aan
S 12
Finite Sum
The equation to find a finite sum
6 + 13 + 20 + 27 + 34 + 41 + 48 + 55 =
nn aan
S 12
Finite Sum
The equation to find a finite sum
6 + 13 + 20 + 27 + 34 + 41 + 48 + 55 =
nn aan
S 12
244614
5562
88
S
How many terms in the sequence?
The sequence totals to 640. Start with 10, ends with 70.
nn aan
S 12
70102
640 n
How many terms in the sequence?
The sequence totals to 640. Start with 10, ends with 70.
nn aan
S 12
n
n
nn
n
16
40640
40802
640
70102
640
Summation Notation
Partial Sum are Finite (Series)
n
n
in aaaa
.......211
Summation Notation
Find n
n
k
k1
90953
Summation Notation
Find n
n
k
k1
90953
nn
nn
nn
nn
1151818
5111818
5112
909
5382
909
2
Summation Notation
Find n
n
k
k1
90953
nn
nn
nn
nn
1151818
5111818
5112
909
5382
909
2
2.20,18
0101518
01818115 2
n
nn
nn
Summation Notation
Find n
n
k
k1
90953
nn
nn
nn
nn
1151818
5111818
5112
909
5382
909
2
termsdecimals no
20.2,- benot can
2.20,18
0101518
01818115 2
n
n
nn
nn
Homework
Page 631 – 632
# 5, 15, 25, 35,
45, 55, 65, 75,
82
Homework
Page 631 – 632
# 10, 20, 30, 40,
50, 60, 70, 80,
90
