Chapter8: Sequences, Series,and Probability
Section8.3: Geometric Sequences And Series
Problem 4ECP: Find a formula for the nth term of the geometric sequence 4, 20, 100, . . . .What is the 12th term...
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Please solve b & f
Transcribed Image Text:12
2
24
DIN-
=3 4² 16:44
2-1=1
3-2-1
3-4--1
4-5=1
5-6 = 1
1. Write the first six terms of each sequence.
3
(a) an =
12 12" 3"
1/2 - 12,3,4, 2 1/2, 3) (d) an-
n²
sp to 9
2!
=2'
(2-1)!
3
1
-1
= 2.1=2
=3-2-1-6
-4.32-1= 24
-5.4.3 2.1 = 120
6.54321=720
9-7=2
11-922
11-13-2
13-15-2
1155=2
12 12
25
+1
(b) an = 3+2an-1,
a₁ = 1
r
12 12:12
6²=36=3
12
F
(c) an = n!
12,6,24, 120, 720
e
e
J
elan = n
(b) 1,
a
1 1 1 1 1
1!
(1-1) =1
n=
2'3'4'5'6
1
an=1
(4)
2(1)-1
(-1) 2
2(2)-1
33
+1
3!
(3-1)!
2. Give a recursive formula and an explicit formula for each sequence.
(a) 1, 2, 3, 4, 5, 6
1 1 1 1 1 1
3' 6' 12' 24' 48' 96
ran+1²an+l, a₁ = 1
(c) 7,9, 11, 13, 15, 17
an=and +2₁ 9₁=7
an-7+2(n-1)
-1
(e) an =
3
2(3)-1.
6-1
-
(d)
n!
(n-1)! Job
(4-1)=4
2/4) -1
7=
(f) annan-1,
a₁ = 10
5
(5-1)
(-1)"
ㅗㅗ
ㅗㅗ
21-171 (-1, 3, 5, 2, - 4.
7.
9.11
J
(-1)
266)-1
(-1)²
2(5)-1
10-1
e an=
7-10-
"
5
12,3,456
(6-1)! = 6
²+2+3
(f) 6, 12, 20, 30, 42, 56-
ran² = an +2n +4
e Tan-n²+3 +2
ran = ½ (a n.₁), 9₁=
e a₁ = ( + )"
(e) 4,6,9,13, 18, 24
r
·|an₁ = (an+n+1)
I
13
1
12-1 =71
1012-12
+ 6+ wh-
126
11
24
6-4 = 2
9-6=3
13-9=4
18-13=5
12-6=6₁
20-12-82
30-20-16
42-30-12
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