Pham, Quoc – Homework 10 – Due: Apr 4 2007, 3:00 am – Inst: Eric Katerman
1
This
printout
should
have
16
questions.
Multiplechoice questions may continue on
the next column or page – fnd all choices
beFore answering.
The due time is Central
time.
001
(part 1 oF 1) 10 points
±ind a Formula For the general term
a
n
oF
the sequence
n
2
,
6
,
10
,
14
, ...
o
assuming that the pattern oF the frst Few
terms continues.
1.
a
n
= 3
n

1
2.
a
n
= 5
n

3
3.
a
n
=
n
+ 4
4.
a
n
=
n
+ 3
5.
a
n
= 4
n

2
correct
Explanation:
In the sequence
n
2
,
6
,
10
,
14
, ...
o
each term is larger than the preceding one by
4, so
a
n
=
a
1
+
d
(
n

1) = 2 + 4(
n

1)
.
Consequently,
a
n
= 4
n

2
.
keywords:
002
(part 1 oF 1) 10 points
±ind a Formula For the general term
a
n
oF
the sequence
n
1
,

2
5
,
4
25
,

8
125
, ...
o
assuming that the pattern oF the frst Few
terms continues.
1.
a
n
=

‡
1
2
·
n
2.
a
n
=
‡

2
5
·
n

1
correct
3.
a
n
=

‡
2
5
·
n
4.
a
n
=

‡
5
2
·
n
5.
a
n
=
‡

5
2
·
n

1
6.
a
n
=
‡

1
2
·
n

1
Explanation:
In the sequence
n
1
,

2
5
,
4
25
,

8
125
, ...
o
each term is

2
5
times the preceeding one,
i.e.
,
a
n
=
‡

2
5
·
a
n

1
.
Consequently,
a
n
=
‡

2
5
·
n

1
since
a
1
= 1.
keywords: sequence, exponential
003
(part 1 oF 1) 10 points
Determine iF the sequence
{
a
n
}
converges,
and iF it does, fnd its limit when
a
n
=
5
n
5

4
n
3
+ 3
5
n
4
+
n
2
+ 1
.
1.
limit = 1
2.
the sequence diverges
correct