MAC 1140 Exam #4

Name: --,--,~----,K--,-=fmMr ljl---____

ID# ------'-'~~______Wl aO\\

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 /24 2 /16 3 /20 4 /10 5 /14 6 /16

Bonus /10 Total I /100 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 nth t erm is given. (5 points)

(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 9 12 15 4' 8' 16' 32' 64' .. .

V\=- \: Q =- "5 =- _ 3-\ • \.j t

h -=-l '. Qz ~ ~ ':.. 2.~~

Q 3.:2­V\=-yQ -: - J., -.- ~

- 3 (I.e, - 2­

_ ' _ rz.. _ -l-j'3h ~y . q~ - ~ - Z~

I S" 3'S­h-=- '5 ~ QS -:: - ~ -:. - 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. 'I ~ ~t:\!. - ;;1('1\ -=- :)(0) -~ ""tIl 0.., :: 31<" - .:2('5) -:0 3( ~) - \0 -= 8~

2. (a) Write out the series. (8 points)

32~ ~ <b I'"-.} -\ +\"'+-\+-u! 01. l . J. . 3· \ .

J. ~ .J...... -1lL. +- .JLI' 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 80th 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 65th 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)

Lt, 7- 0 q3 ::~2(- {') ~ EI1 Q'1 :: -~(-~)::~

qs :: ~(- ~){ il (b) Find the rth and write a formula for the nth term of the sequence

~, ~,3, .... (6 points)

",:\-1a :: ~ . (i) 1­

6. Find the sum of each series. (8 points each)

(a) (l)k-l002: 10 . "6k=l

(0 - b C,oto - ~ -;:-:::0­£ .i ;:) ~

(b) 64 + 16 + 4 + 1 + ...

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Bonus. Represent the repeating decimal 0.63 as a fraction.

O.Co:; =- O.Co3333 . __=0.<0+ o.o3.f 0 . 00"3+ O.OD03f -- ­

- Co+3- 4l -t 3 . f - 70 {em 1000 (0,000

(0 - (0' + ---­

\ - ;0 .

co -'I-+(0.,

- {If 3-..+­1Q 70