Some sequences are defined by a recursion formula —that is, a formula that defines each term of the sequence in terms of one or more of the preceding terms. For example, if { a n } is defined by a 1 = 1 a n d a n = 2 a n − 1 + 1 f o r n ≥ 2 then a 2 = 2 a 1 + 1 = 2 ⋅ 1 + 1 = 3 a 3 = 2 a 2 + 1 = 2 ⋅ 3 + 1 = 7 a 4 = 2 a 3 + 1 = 2 ⋅ 7 + 1 = 15 and so on. In Problems 63–66, write the first five terms of each sequence. 63. a 1 = 3 and a n = 2 a n – 1 – 2 for n ≥ 2
Some sequences are defined by a recursion formula —that is, a formula that defines each term of the sequence in terms of one or more of the preceding terms. For example, if { a n } is defined by a 1 = 1 a n d a n = 2 a n − 1 + 1 f o r n ≥ 2 then a 2 = 2 a 1 + 1 = 2 ⋅ 1 + 1 = 3 a 3 = 2 a 2 + 1 = 2 ⋅ 3 + 1 = 7 a 4 = 2 a 3 + 1 = 2 ⋅ 7 + 1 = 15 and so on. In Problems 63–66, write the first five terms of each sequence. 63. a 1 = 3 and a n = 2 a n – 1 – 2 for n ≥ 2
Solution Summary: The author explains that the first five terms of the sequence a_n are 2, 4, 6, 10 and 18. Since the value of n starts from 2, compute the term for
Some sequences are defined by arecursion formula—that is, a formula that defines each term of the sequence in terms of one or more of the preceding terms. For example, if {an} is defined by
a
1
=
1
a
n
d
a
n
=
2
a
n
−
1
+
1
f
o
r
n
≥
2
then
a
2
=
2
a
1
+
1
=
2
⋅
1
+
1
=
3
a
3
=
2
a
2
+
1
=
2
⋅
3
+
1
=
7
a
4
=
2
a
3
+
1
=
2
⋅
7
+
1
=
15
and so on. In Problems 63–66, write the first five terms of each sequence.
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39. The balls shown have different masses and speeds. Rank
the following from greatest to least:
2.0 m/s
8.5 m/s
9.0 m/s
12.0 m/s
1.0 kg
A
1.2 kg
B
0.8 kg
C
5.0 kg
D
C
a. The momenta
b. The impulses needed to stop the balls
Solved 39. The balls shown have different masses and
speeds. | Chegg.com
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13. In 2000, two organizations conducted surveys to ascertain the public's opinion on banning gay men from serving in leadership roles in the Boy Scouts.• A Pew poll asked respondents whether they agreed with "the recent decision by the Supreme Court" that "the Boy Scouts of America have a constitutional right to block gay men from becoming troop leaders."A Los Angeles Times poll asked respondents whether they agreed with the following statement: "A Boy Scout leader should be removed from his duties as a troop leader if he is found out to be gay, even if he is considered by the Scout organization to be a model Boy Scout leader."One of these polls found 36% agreement; the other found 56% agreement. Which of the following statements is true?A) The Pew poll found 36% agreement, and the Los Angeles Times poll found 56% agreement.B) The Pew poll includes a leading question, while the Los Angeles Times poll uses neutral wording.C) The Los Angeles Times Poll includes a leading question, while…
A tank contains 60 kg of salt and 2000 L of water. Pure water enters a tank at the rate 8 L/min. The
solution is mixed and drains from the tank at the rate 11 L/min.
Let y be the number of kg of salt in the tank after t minutes.
The differential equation for this situation would be:
dy
dt
y(0) =
Chapter B.1 Solutions
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