MAC 1140 Exam #4
Name:
ID#
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HONOR CODE: On my honor, I have neither given nor received any aid on this
examination.
Signature: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __
Instructions: Do all scratch work on the test itself. Make sure your final answers
are clearly labelled. Be sure to simplify all answers whenever possible. SHOW
ALL WORK ON THIS EXAM IN ORDER TO RECEIVE FULL CREDIT!!!
No.
Score
1
2
/24
/16
/20
/10
/14
/16
/10
/100
3
4
5
6
Bonus
Total
I
I
1.
(a) Write down the first five terms of the sequence. (5 points)
{ ~}
n+l
(b) Write down the first five terms of the sequence whose general
is given. (5 points)
nth
t erm
(c) The given pattern continues. Write down the formula for the general
nth term of the sequence {an} suggested by the pattern. (6 points)
3 6
4' 8'
=- _
V\=- \: Q =- "5
•
~
V\=-yQ
-: - 3
_ '
':..
15
64' .. .
3 -\
t
\.j
h -=-l '. Qz ~
9 12
16' 32'
2.~~
Q
J., - . -
3.:2­
2­
(I.e, -
_ rz.. _
h ~y . q~ - ~ -
I S"
'3 -l-j
Z~
h-=- '5 ~ Q -:: - ~ -:. S
~
3'S­
2b
(d) A sequence is defined recursively. Write the first five terms of the
sequence. (6 points)
Ql~m
Q1- ";. 3Q I - J(-2) == 3 (:il - '1
=-0
a -:. )~"t - ~(~);::. ~lo) - I.- =- @
~
a. ~ ~t:\!. - ;;1('1\ -=- :)(0) -~ ""tIl
'I
0.., :: 31<"
- .:2('5) -:0 3( ~) - \0 -= 8~
2.
~
~
(a) Write out the series. (8 points)
<b
I'"
32
- .1} - \ +\"'+-\+-u!
0.
l . J. . 3·
\.
J.
~
.J...... -1lL. +- .JL
I'
t~.\- ;2, . \ +- ~-2- t
If·1· 1· \
l
:I. 1-4
~ t +~ ~
*]
(b) Write the series using summation notation. (8 points)
1
4
9
16
25
-+-+-+-+­
5 6 7
8
9
3. Find the sum of each series (using the sum properties and the sum formulas).
(10 points each)
(a)
(b)
k=4
4. (a) Find the 80 th term of the arithmetic sequence {an} whose initial term
is al = 8 and whose common difference is d = 7. (5 points)
G:~ =- (t ~ (t\-\)d
Lito = ~ f (tD -I)l
-:: ~ * i1 ·1­
-= ~ -\-~~
:c§
(b) Find the 65 th term of the sequence. (5 points) -13, -7, -1, .. . 5.
(a) Write the first five terms of the geometric sequence whose second term
is a2 = 32 and whose common ratio is r = - ~. (8 points)
0
Lt, 7-
q3 ::~2(- {') ~
EI1
Q'1 :: -~(-~)::~
qs ::
il
~(- ~){
(b) Find the rt h and write a formula for the
~, ~,3, .... (6 points)
a : ~ . (i)
",:\-1
1­
nth
term of the sequence
6. Find the sum of each series. (8 points each)
(a)
2: 10 .
00
k=l
to
-£ .i
(0
~
-b
~
(l)k-l
"6
-;:-:::0­
;:)
C,o
(b)
64 + 16 + 4 + 1 +
--
...
Bonus. Represent the repeating decimal 0.63 as a fraction.
=
O.Co:; =- O.Co3333 . __ 0. <0+ o.o3.f
-
Co+3- 70
{em
4 l -t
1000
(0
3 .f
(0,000
- (0' + - - - ­
\ - ;0 .
co -'I
-+
(0.,
-
{If
3
-..+­
1Q 70
0 . 00"3+ O. OD03f -- ­