MATEMÁTICA – PROF. MURILO DUATTI LISTA DE EXERCÍCIOS – PROGRESSÃO ARITMÉTICA – 2º ANO A, B, ETIM DATA DE ENTREGA: 070!20"# – MÉDIA DE 3,23 EXERCÍCIOS / DIA COMEÇANDO EM 24/02 ". $%&' ( )*+-+*( -*( /-&+1( & PA: 3"02, 45, 6,...89
2. $%&' ( )*+-+*( -*( /-&+1( & PA: 30, #!, 5,...89 !. D(+; <+<'+;&; -;=( - >&;-; +;+/&; - )*-)&*&?=(. O +<( -;;-; &'-&; -'&@(*& % )'&/-&-/( - *-+/&-/( )&*& &@(;, -;&@-'-<-/( ( ;-%+/- -;%-&: ciclista sta 1: +/+< cicli +/+<+& +&** ( *-+ *-+/& /&-/ /( ( <( <( 5 - )-*< )-*<%* %*;( ;( - &%&%-/ /&* &*,, & <&& <&& +&, +&, ! & &+; &+; )&*& )&*& ;-*;-*- )-*< )-*<(* (**+ *+( (; ; ciclista 2: +/+<+&* 2: +/+<+&* ( *-+/&-/( <( 2# - )-*<%*;( - &%-/&*, & <&& +&, 2 & &+; )&*& ;-*- )-*<(**+(;. S&@-/(;- %-;;-; -;;-; <+<'+;&; <+<'+;&; +/+<+& +/+<+& ( *-+/&-/ *-+/&-/( ( /( -;( +& - %- ( *+/( *+/( -;;- *-+/&-/( *-+/&-/( ;- %&/( (; &'-&; &'-&; )-*<(**- )-*<(**- & -;& +;H/<+& - % -;( +&, )(-;- &>+*&* %- &( >+/&' ( *-+/&-/( ( <+<'+;& " )-*<(**- %& +;H/<+& (&', - , -: a) 76"
@8 7"5
<8 656
8 4"#
5. D&& & )*(*-;;=( &*++<&, 3"!, 20, ...8. E/=( & ;(& -;- ( !0 & ( 52 -*( : &8 !04
c) !!#5
@8 50"2
8 !#5!
-8 5"02
#. JNK-*(; *+&/%'&*-; ;=( /K-*(; %- )(- ;-* *-)*-;-/&(; )(* )(/(; &**&/&(; /& >(*& - *+H/%'(; -%+'-*(;. E <(/1-/+-/- ->+/+* " <(( ( )*+-+*( /%-*( *+&/%'&*. A)*-;-/&(; A)*-;-/&(; & ;-%+* (; )*+-+*(; /K-*(; *+&/%'&*-;. S- T *-)*-;-/& ( / ;+( ;+( /K-*( /K-*( *+&/%'& *+&/%'&*, *, -/=( T1 ! 1, T2 ! 3, T3 ! ", T5 "0, - &;;+ )(* +&/-. O 1&'(* - T100 +%&' &: a) #.0#0
@8 5.4#0
8 ".5#6
-8 724
<8 2."67
. A ;(& - ((; (; +/-+*(; -/*- #0 - !#0 %- )(;;%- ( &'&*+;( &; %/+&-; +%&' & " : &8 5#
@8 5677
<8 #206
#) #660 #) #660
8 ##!4
7. S- 3&, @, <8 %& PA - *&=( $ , & ;-%/<+& 3&2, @2 * 2, <28 : &8 U& PA - *&=( * 2
@8 U& PA - *&=( @Q*
8 U& PG - *&=( * 2
-8 U& PG - *&=( @Q* 2
c) U& c) U& PA - *&=( 2Q@Q*
6. U& <()-+?=( -;)(*+1& - *-&'+&& - / - / &/(; 3/ +/-+*( - &+(* %- "8. S&@-;- %- (%1- <()-+?=( /(; &/(; - "4!", "4#4 - "445. A;;+/&'- & &'-*/&+1& %- &)*-;-/& & )*+& && -;;& <()-+?=( & )&*+* -;- &/(. &8 20"0
@8 20"2
<8 20""
%) 2006
-8 2004
4. O; <(-'(; ;- *-)*(%- &+; *&)+&-/- %- & &+(*+& (; &>-*(;. C(/;+-*- %& <('V/+& - <(-'(; %- ;- +/+<+& <( % 1, a2 ! 1 -, 1 -, )&*& / W K/+<( <&;&' - <(-'(; &%'(; - -/(- ) (* a ( /K-*( - <&;&+; &%'(; -;& <('V/+& &( >+/&' - -;-;. S- a1 ! 1, 2, a&1 ! a & a ' 1, ( /K-*( - <&;&+; - <(-'(; &%'(; /& <('V/+& &( >+/&' ( %+/( ; ;-*: &8 "!
@8 6
<8
%) #
-8 5
"0. E %& )*(*-;;=( &*++<& 3a 3a1, a2,(((, a), & ;(& (; / ) *+-+*(; -*(; && )(* S ! * & , , ;-/( @ % /K-*( *-&'. S&@-/(;- %- &! 7, --*+/-: &8 ( 1&'(* - @ - & *&=( & )*(*-;;=( &*++<&. @8 ( 200 -*( & )*(*-;;=(.
<8 & ;(& (; 20 )*+-+*(; -*(; & )*(*-;;=(. "". N% )*(*&& - <(/+<+(/&-/( >;+<( % &'-& <(**- ;-)*- !00 -*(; & &+; ( %- <(**-% /( +& &/-*+(*. S&@-;- %- /( ;-%/( +& -'- <(**-% % %+'V-*(. E/=(, /( <+( +&, -'- <(**-*: &8 !.700 -*(;
@8 !."00 -*(;
c) !.500 -*(;
8 5.000 -*(;
-8 2.600 -*(;
"2. N%& P.A. P.A. - *&=( #, ( )*+-+*( -*( 5. $%&' & )(;+?=( ( -*( +%&' & 559
"!. C(/;+-*- & ;-%/<+& (; /K-*(; )(;++1(; )&*-;, <('(<&(; - (*- <*-;<-/-. C&'<%'- 4#º -'--/(. &8 4#
@8 "!"
%) "64
<8 "67
-8 "4"
"5. N%& P.A., <%( 2º -*( +%&' & # - ( º -*( +%&' & "! ( 20º -*( +%&' &: &8 "!
c) 5"
@8 50
"#. O; /K-*(;
"0 T
,
x
− 3 -
x
8 52
-8 /&.
+ 3 ;=( (; ! )*+-+*(; -*(; - %& P.A., - -*(; )(;++1(;, ;-/( ≠0. O <+( -*( -;&
P.A. +%&' &: &8 #0
@8 #!
<8 #5
". A ;(& (; -*(; - %& P.A. && )(* S n = n a) "6 @8 40 <8 6
2
−
n , / ", 2, !,... E/=( ( "0( -*( & P.A. 1&'-: 8 "00 -8 4
"7. A ;(& (; "" )*+-+*(; -*(; & )*(*-;;=( &*++<& ∈ IN -(;: a)
a n
= 3n − 2
@8
a n
= 2n − 3
<8
#) ##
8 #7
a
n
( a1 , a 2 ,..., a ,...) "7. Sn
=n+3
8
a n
& ""
= 2n + 3
=
&"
-8
+
a n
!0 -/=(, )&*& %&'%-*
= 3n + 2
"6. N%& P.A. - -*(;, & ;(& ( )*+-+*( <( ( - (*- "20. A ;(& ( ;-( -*( <( ( - (*- / – # : a) "20
@8 0/
<8 40
8 "203/"8Y/
"4.3MACZ8 S- >3/8, / ∈ Ν %& ;-%/<+& ->+/+& )(*
&8 #47
f (0) = 1 f (n + 1) = f (n) + 3
c) 0"
@8 00
8 05
-8 "20/
, -/=( >32008 :
-8 07
20. 3FU[EST8 S-& &, @, < *; /K-*(; -;*+&-/- )(;++1(; - )*(*-;;=( &*++<&. S- & *-& ( *+H/%'( ABC, <%(; 1*+<-; ;=( A3&,08, B30, @8 - C3<, 08, +%&' & @, -/=( ( 1&'(* - @ : &8 #
@8 5
<8 !
#) "
8 2
2". A<- &" /%& P.A., ;&@-/( %- $ ! 1/4 - a1+ ! 21. 22. O; H/%'(; +/-*/(; - % *+H/%'( -;=( - )*(*-;;=( &*++<& - ( -/(* -'-; & -&- ( &+(*. O &+(* H/%'( ( *+H/%'( --: &8 0(
@8 7#(
c) 60(
8 40(
-8 "20(
23( S- - %& P. A. - *&=( )(;++1& ( )*(%( (; *; )*+-+*(; -*(; !65 - & ;(& 25, -/=( ( %&*( -*( : &8 0
@8 5
<8 6
#) "
8 "2
25. 3ITA8 $%&/(; /K-*(; +/-+*(; -+;-, - "000 & "0000, %- /=( ;=( +1+;1-+; /- )(* # /- )(* 7 9
2#. C(/;+-*- & ;-%/<+& 3", 2, 5, #, 7, 6, "0,"",...8, <%(; -*(; ;=( (; /K-*(; +/-+*(; )(;++1(; %- /=( ;=( K'+)'(; - !. A ;(& (; %&*-/& )*+-+*(; -*(; -;;& ;-%/<+& : &8 00
c) "200
@8 400
8 "500
-8 "600
2. A; -+&; ( '&(, & +&(/&' - & *-& - % %&*&( -;=( - P.A., /-;;& (*-. O '&( ( %&*&( --: &8
2
) 2
2
−
1
<8 1 +
2
8 5
-8
2
2
27. 3FU[EST8 S-& A ( <(/%/( (; "44! )*+-+*(; /K-*(; +/-+*(; -;*+&-/- )(;++1(;. &8 $%&/(; K'+)'(; +/-+*(; - "# )-*-/<- &( <(/%/( A9 3R: "!28 @8 $%&/(; /K-*(; - A /=( ;=( K'+)'(; +/-+*(; /- - ! /- - #9 3R:"0!8
26. A ;(& - ! /K-*(; - P.A. "# - & ;(& - ;-%; %&*&(; "07. O -/(* -;;-; /K-*(; : ) "
&8 5
<8 #
8 4
-8"0
24. N%& -;*&& -+;- (+; -'->(/-; +/;&'&(; /( &<(;&-/(: % /( %+'(-*( ! - (%*( /( %+'(-*( 66. E/*- -'-; ;-*=( <('(<&(; &+; " -'->(/-;, &/-/(;- -/*- (+; -'->(/-; <(/;-<%+1(; ;-)*- & -;& +;H/<+&. D--*+/- - %&+; &*<(; %+'(*+<(; -1-*=( >+<&* -;;-; /(1(; -'->(/-;. !0. D--*+/- & +& &*++<& (; ;-+; -+(; &*++<(; %- )(- ;-* +/-*)('&(; -/*- "0 - #00. !" $%&' & ;(& (; /K-*(; +/-+*(; - " & !#09 !2. $%&' & ;(& (; "20 )*+-+*(; /K-*(; )&*-; )(;++1(;9
!!. D--*+/- & P.A. - %- ( 1+;+( -*( 2 - & ;(& (; #0 -*(; +/+<+&+; #0.
!5. $%&' ( 2!º -'--/( & P.A. - *&=( ! - %- & ;(& (; !0 -*(; +/+<+&+; 2##9
!#. N%& )*(*-;;=( &*++<& '++&& - %- ( "º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
@8 /(; ;-+; +&;.
!4. 3UER]8 O@;-*1- & &@-'& - P+(*&;: A ;(& - ((; (; /K-*(; -;& &@-'& & & 1+;+& '+/& ;-*9 (
50. 3ENEM8 O *>+<(, (@+( & )&*+* - &(; ( M+/+;*+( ( M-+( A@+-/-, (;*& ( <*-;<+-/( ( /K-*( - -;)<+-; & >&%/& @*&;+'-+*& &-&?&&; - -+/?=(. S- &/+&, )-'(; )*+(; &/(;, & -//<+& - <*-;<+-/( (;*&& /( *>+<(, ( /K-*( - -;)<+-; &-&?&&; - -+/?=( - 20"" ;-* +%&' &:
3A8 5#
3B8 54!
C) 546
3D8 #!6
3E8 44
5"( ENEM 320"08 O *&@&'( - -)*-;&; - -+- (; )*(>+;;+(/&+; <(/-<+-/(; - +>-*-/-; *-&;. N& ;-&/& )&;;&&, ((; (; >%/<+(/*+(; - %& -;;&; -)*-;&; -;&1& -/1('1+(; /& &*->& - --*+/&* & %&/+&- - -;*-'&; %- ;-*+& %+'+&&; /& <(/>-=( - % )&+/-' - N&&'. U (; >%/<+(/*+(; &)*-;-/(% % -;@(?( &; )*+-+*&; <+/<( '+/&; ( )&+/-', %- -*, /( (&', "#0 '+/&;.
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