Sequences

1
Sequences
2
Sequences
19 22 25

• 4, 7, 10, 13, 16, ___, ___, ___
• Arithmetic Sequences have a common ___________
• 3, 6, 12, 24, 48, ___, ___, ___
• Geometric Sequences have a common
  __________
• 1, 4, 9, 16, 25, 36, 49, ___, ___, ___
• 1, 8, 27, ___, ___, ___
• 1, 1, 2, 3, 5, 8, ___, ___, ___

difference
96 192 384
ratio
64 81 100
64 125 216
13 21 34
3
Sequences
Arithmetic
25 30 35

• 5, 10, 15, 20, ___, ___, ___
• 3, 7, 11, 15, ___, ___, ___
• 8, 2, -4, -10, ___, ___, ___
• These are Arithmetic Sequences.
• They each have a common __________.

19 23 27
-16 -22 -28
difference
4
Arithmetic Sequences
4 7 10 13 16
a1
a2
4 3
(1)
4
a3
4 3 (2)
a4
4 3 (3)
a5
4 3 (4)
(n-1)
a1
an
d
a100
4 3(99)
301
5
Arithmetic Sequence
6
Arithmetic Sequence
Find the 68th term of an arithmetic sequence
with a first term of 16 and common difference of
-9.
a68 -587
7
Arithmetic Sequence
Find n for the sequence in which d 4, a1 4
and an 76.
19 n
8
Arithmetic Sequence
Find the common difference with a first term of
22 and 29th term of 33.25.
11.25 28d
45/112 d
9
Arithmetic Means

• Means are terms that are
• in between other terms!

Find four arithmetic means for 2 and 87.
2, ____ , ____, ____, ____ , 87
19
53
70
36
a6
a1
10
Arithmetic Series

• Story of Carl Friedrich Gauss
• 1 2 3 4 97 98 99 100
• Number of Pairs times the Sum
• of the first and last terms

11
Sequence and Series

• Arithmetic Sequence

• Arithmetic Series

12
Arithmetic Series

• Find the sum of the first 40 terms in the series
  8 14 20
• S40
• a40

13
Sequences
Geometric
625 3125 15625

• 1, 5, 25, 125, ___, ____, _____
• 1/3, 1, 3, 9, ___, ___, ___
• 4, 2, 1, 1/2, ___, ___, ___
• These are Geometric Sequences.
• They each have a common __________.

27 81 243
1/4 1/8 1/16
ratio
14
Geometric Sequences
3 6 12 24 48
a1
a2
3 2
1
a3
3 22
a4
3 23
a5
3 24
a1
r
an
(n-1)
a10
3 29
1536
15
Sequence and Series

• An Arithmetic Sequence has a common _________

• A Geometric Sequence has a common _________

16
Sequence and Series

• Geometric Sequence

• Geometric Series

17
Sequence and Series

• Infinite Geometric Series

What happens to ?
18
Sequence and Series

• Infinite Geometric Series

Important Note
19
Sequence and Series

• Find the sum
• 421.5.25.125

• Use