Ans,rsn Key
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HOMEWORK
MA40: ALGEBRA 2
1.7
ffi
lllichigan Stadium Problem (Arithmetic Series)
-
Find S, for each arithmetic series described.
1) 7 +t+(-s)*(-tt)+ ... n=21
Ari*\6erl;6 $er'eg , 5n= n
" fo,=*on)
La
a,, ?, d= -0r n=JI
ser = (r,)(r-#:))
i" -2r.r;",'y;
a'zr
Q. = O. 1 1n-i) d
tii;n'
l3o,==l :
96 = l{d
n
=25
sn = h
d 75, n=16,
an
Arr$rrnet;c $e,rtca
=
Qro
dii,:;
.ll:,\itb'd'5 5,u-.(tD(#)
;l=;, s lrr'-r)1s)
7a-'d', +75
r lq(-3)
Sa,
= -17
^"A,aa.5n-
= a3!
t
[,lsr'l-t=,1 -*=\ry)
q'
.l
l
5,rr, 55
4,= -3
to
6) oo=5n*1 n=13 -n /a,lg)
n.,-.*,, $gtle5 S,l = (-
='3n=n(q9
7]. =o,+t5(5)
9n= fl
Qr=10, n=70 td='3
qn= q, t Cn- r)d
Qro z tlo t(ao-l)t-3)
l5r,
= lsoo\
I--1
d ='1
ar=4A, n=20, d =-3
Arilhrnefic SecEs
c)e5\a
= ]sI1ll]oo)
n =12
=G
4)
(tI5)
6+1.4+8.8+10.2+11.6+ ...
| (tl-lItY)
-61(tt)tl.t)
Q'*: Jl't
0l -- -l13
3) at=4, ar=100,
Ac,l+rr"ret, c Seies
Q, -- i, OrS : tOO, n : ]1
Pedod:
2)
0rI
--iifi';?[f)
5)
Name:
|,.': 5(3)'l
z
6{
|
= 'l 'f
Write the terms of each series and find the sum.
8)
7') Zb* -r)
I
=Lr,l.t -l1ref-!* Lr (rlil
: (t(,)-D +(at'r)-r) -i"o:
-
!i,', .'l
+
[x(5)'-
f6*u;
gerile-
Ari*,"",cTi6
r]
+
(r+rts))t(r+gt'))+ [r+ttd)t;"
) ir+r$ f (l+lr) + (r+v011 "'
laJs 4 jq
,
= l+ 8Bq) "' 2tZ
h=(3q-3)+l=
3?
7,^u+l?3\
1n=nffi SriG)[-/=
t8
+
l' r u))t (rLtr'
t(*alD
l=3, Or= f +6,1S1=.15
I:iql?l#lP-''
e) I(t.t + a.ak) =(t.t
(Hr(3'rD
t''' t(s'rt {' r(' o1
ol
4/61
t [o - ir) = (o-itl) + (6-{t:r)+(o'}o}+"'* (e-id
L?**rr
Ar.+r,*etil=lrie I
+ (e- fl_
(g,t + l1 7)) = (6-?)-(6-*)(, +)*,,,
t s. d + "' v* (g,l*fi
tt) t [r. ]G..r) {6.1
{6. tm.c)+
i=S,05:5,1 +l,lO=30.1 = (8,i,t rt )2)r[f.r+)G.r)
)
-Z) *
gjgr.' + (3-'+)
.
=G
[=lt, ey6 = 8,1 +{,1(rt) 87J
+l
r
n = (rt-$+l =ltl
S^=
r
+
(Ai
I
lFi*f;n
;t8il3/r;
s,,r=(o(ry)
I
^(t*)
"+-4
+r@Hffi
11)
The first row of a concert hall has 25 seats, and each row after the first has one more seat than
the row before it. There are 32 rows of seats.
a. Write a rule for the number of seats in the n'h row.
0n=O,+ (n-r)l
Afilht',alic,,
Qr =
d=
15
,= 15
n=iz
r (n-r)(r)
= e5 t n-l
|
0n= n+
Aq
b.
35 students from a class want to sit in the same row. How close to the front can
L)a^^l o- rov) r.pifl-r at leust On = h + aY
6" a)l 35 s*ode"ts +o Sttrn
35 Seatsr so frnat no
+)L{
n
3F =
the Sawr ( rour) t\e close s*
*hey cqn be *a -lho €ra"t
Nhe"{'
0n=35
y\=ll
c. What is the total number of seats in the concert
is rar^,r ll
hall?
rk- h+0\
Qt=)S,n=31 (_
Jlt'=(Zi(W1
Ariil'''molic Senes G*=n irq
or;^==rllr, s*= Dqb
an =,
8duport+het?1-s
af
Seats in *he carce,*l
(+)
d.
number
hull
is
teqb,
--H;(ry)
S,r:a;) (ry l#;r':llt,u'
H,rffifry)
5n=n(ry)
Suppose 12 more rows of seats are built (where each row has one more seat than the row
before it). How many additional seats willthe concert hall have? ,__ . ,
,p".+,i s:";;;;
$e.ric5
Arilh'natig
-'
s}+s
r= 33
r^rll add 750 SeatS
= 1e0
n--9,i,Gq,r=[ut)+)r = 68
n=81-g:)|l = l1
12) A rocket rises 20 feet in the 1$ iecond, 60 feet in the
a.
(scc1
Tme
second, and 100 feet in the 3d second.
lf it continues at this rate, how many feet will it rise in the 20h second?
2nd
Qe-01=60-)D:LlD Qn=4,+(n-r)d f'
1l )13
Qs -a>=100 -60 { 0
- I I
[l= ?0r $rnc( oq =o3p I
seq
0ro = io + fao-r)(qD
0 I Co I roo Acitxr..ct\c
/
=
ih th\'5
intCf/a
(ttc+)
I
b.
?D
/
0r = 10, d =
= )01
ground will it be after
high
above
rate,
the
it
at
this
how
lf continues
ffi,)['affi:"lj:j;;;
5n=
r(ty)
3^=3],=,,,
(rqXqo)
s,o =
13) evauar"
(* * YY
-l
n: ao
*n"n *
; -' try =,j,"- 1' r=-L
_l-l
ta)
Tffi
r t4)l
(-r)
=
780 {cev rn *hc
)g{. Qconol
= 9000
Afle" )D 1e(ot
ffinefo6cr
'rii'o [-
r3
=!i'y=*r'
rooKel tpitl rise
)o(ry
clooo
€""i
it, qrono!
ustiff your answer by shouing
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