2026北师大七年级数学上举一反三：专题02 有理数中的规律(代数推理)问题(专项训练)(原卷版)

专题02有理数中的规律（代数推理）问题（举一反三专项训练）



2024



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【题型1数字规律】

%1

&24-25'()*·+,-.·!/0121,3,7,15,31…345627812(19397):8;2

(19397915):8<2(19397915931):…3=>5:?8112@ABCD&0

A7213−12B7214−15C7213−14D7214−13

EF1-1

15G31:−2:3:−4:5:−6……HIJ:?82021KD&0

A72021B7−2021C72022D7−2022

128

EF1-2

&24-25L()*·MNOPQR·!S0TU2

9919…V=:86KW7

235

EF1-3

&23-24'()*·XYXZ·!/01:2:4:8:16:…:W31[>5H12:?8

2017KW&\\0

A722015B722016C722017D74032

【题型2数阵规律】

%2

&23-24'()*·MNO]^O·!/0_`<a:bcde<a$:fgh<a$&126101I

/ijH<a$kl;mFCHno:pqrHstuvwx<yz(7

3=>5:8'{8|KHs}~8{8<KH€W&\\0

A7−700B7700C7−420D7420

EF2-1

&23-24()*·+,‚ƒ·!S0„…†‡ˆ>‰1K<a$:

3Š‹*>5H,?810{ŒŽH83KW7

EF2-2

&23-24()4·MNOPQR·

‘’0TUj@“H<a$:?87{H”•1K

W7

EF2-3

TU4–12

−1:2:−3:4:−5:6:…:„—2>‰jH$F:3Šj>4

˜810{Œ™89KW&0

A7−90B790C7−91D791

【题型3数表规律】

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„š›3‹4>5:?2016@œHž（）

815825835845…

81{12910

82{43811

83{56712

84{16151413

85{17…

…

A7845{8105B7810{8455

C7844{8105D7810{8445

EF3-1

&23-24'()*·Ÿ

¡¢·!S0TU/“£”$/¤B¥H:¦GTU§H:

¨©bHªD7

EF3-2

«œ4–<K¬­®HAstH:¦G=:CHªW&0

A776B782C786D7108

EF3-3

&23-24'()*·O¯°±·²³´µ0123/ŒŽV¶>5:?89K/

m+n=&\\0

A7100B795C790D785

【题型4数图规律】

%4

&24-25()*··¸·!/0j:i­stH¹º»‰12¼:¼½w6¦¹º:

¼½w10¦¹º:¼½w14¦¹º:…:3=:?88K$/½w¹ºH¦W&①0

②③

A732B734C736D738

EF4-1

&23-24'()*··¸¾¿À·!S0j:i­stH¹º»‰12¼:81K¼½w

3¦¹º:82K¼½w5¦¹º:83K¼½w7¦¹º:…:3=:?82024K¼/½w

¹ºH¦W&0

A74047B74048C74049D74050

EF4-2

&2025··¸Z·;Á0jWi¹sÂHÃaÄ31[ʼnH12¼:8K¼

/A4ÆÃaÄ:8K¼/A7Æ:8K¼/A10Æ:…:3=>54˜:8K¼/①

ÃaÄHÆW0&②0③⑧

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aaa

EF4-3

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a

A7¦……Š=»4˜:7HÊ˺¦W&0¦

A723B763C7127D7129

【题型5运算规律】

%5

&23-24'()*·ÌÍÎÏ·²³´µ0TU4–HFÐH>5:J©Ñ•–HFÐ

234

2+2=22×:3+3=32×:4+4=42×:7

33881515

EF5-1

TU45Қ›HFÐ

4×12−12

4×22−32①

4×32−52②

…③

¦G*Ó:?82018KFÐHªW（）

A78068B78069C78070D78071

311311311

EF5-2

&23-24'()*·ÔÕÖ×·²³´µ0TU45FÐ

a==−Øa==−Øa==−Ø

11×41424×74737×10710

311

a==−Ø…:3=:Ùa+a+a++a=7

410×1310131232023

⋯

EF5-3

&22-23'()*·ÚÛCÜ·!/0TU45¤FHÙÝÞ

11313

1−=1−==×Ø

224422

11824

1−=1−==×Ø

329933

111535

1−=1−==×Ø

42161644

112446

1−=1−==×Ø

52252555

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1

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1−=×7

102

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11111

(1−)×(1−)×(1−)×...×(1−)×(1−)=7

2232422020220212

【题型6周期规律】

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àáâãäåæ(Bi)ç#{èE:鶜1K!ê:èEHëW*1¶ëH1ì7æH!&ì

è!W1¹í7îïA1ðHñèEHæ:?1¹í•A0.5ðuòóèE:ôõ1¹íbA0.25ðuò

óèE:èE1ö3Š—áuò4˜:÷ø5¹í•:ùAzúðæuòóèEû&0

131151

7777

A32B32C16D16

EF6-1

üHýþ1™A<áÿ:V¶3Š2Āāÿ93ĀĂÿ92ĀăÿHĄą>57ĆćŒ8

1ĀĂÿĈ:8125ĀÿW&0

A7ăÿB7ĂÿC7āÿD7°ĉĊ[

EF6-2

0TU45F

21=2:22=4:23=8:24=16:25=32:26=64:27=128:ċõTU:iß@uv

HĊ[22011HKW&\\0

A72B74C76D78

EF6-3

&24-25'()*·ÔÕČč·²³´µ0ĎďĐ(ĉW/đĒĉ*šē‹Ĕĕ1öĖiHĐ(o

ĉ7ĎďWÚĎCėďHĘc:“ę9Ě9ě9Ĝ9ĝ9Ğ9ğ9Ġ9ġ9Ģ”ģKĤÚĎØ“Ð9ĥ9Ħ9

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ěĦ…0‡IJLģD1!:ijĴĈ:ĵĶķĸ:—ĕWĹcH“Ďď”:

Ē(ĺĻ<:ļģĽW

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【题型7递进规律】

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&24-25'()*·ń¢¢Ņ·²³´µ0j:ņ*O:AŇňHʼnŊD12:1ŋňPŒňA©u:

AOAAAOAA

3‹4Ōŋ

81¶Ōŋ§H/ň1ō:82¶Œ1ňŌŋ§1H/ň1ō:83¶Œ2ňŌŋ

AOAAAAAnn

§2H/ň3ō73Š—ŎHŏŐŌŋ§ň4,5,6n&≥3:Wő0ō:øŒõ—Ŏ2024¶Ō

AAA

ŋ•Hň2024~1H/ňHʼnŊW&0⋅⋅⋅

1111

A712−3×B79−3×C712−3×D79−3×

22022220222202322023

EF7-1

&24-25'()4·…đ·œ!Ŕŕ0‡o$1Ŕj4ŖŔ

81¶

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A712B713C714D715

EF7-2

j:ņ*Ň[ňA9BŞŃH6ŗDş18C14:vœAę9ĚŇŠšÐŢţ6ŗŒA9B

tí©u:ŤťņŦ{:ŧŨ6ŗDéũ175KŪC177KŪ:Ñū81¶sŽŦ{1ũ:8;

¶}ŽŦ{2ũ:8<¶sŽŦ{3ũ:8|¶}ŽŦ{4ũ:8ösŽŦ{5ũ:……:3j=:

?Ñū81¶sŬ@½Hí¥D&0

A755ũB7190ũC7200ũD7210ũ

EF7-3

&2025·Ņŭٟ·ÁÇÈÉ0„1ů™<a$Űű6‰|K¹9$Ų1ŎH™<a$&j

@“0:ķD81¶ŖŔ:›•„ų/4aH™<a$b3tŎHoĉ6‰|Ŵ6:ķD82¶Ŗ

Ŕ7ŝé¶ŵݏ4aH™<a$3=oĉ6‰|Ŵ6:j=ĵĶ#{4˜7

(1)ŝŖŔ4¶:?ĘùŶŚ§_____K™<a$7

11

(2)Ù+1+1+1+1+1+1+Hª7

48163264128256512

【题型8数形规律】

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jWŷŸÝŹõź“Ż:1ŠŷŸĺ‹ODżňÝLŽžOA:OB:OC:OD:OE:OF