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1、八种数列及其变式1、等差数列例题:12,17,22,27,(),37解析:12172227()37↘↙↘↙↘↙↘↙↘↙55555公差为0,形成一个常数数列答案:后一项与前一项的差为5,括号内应填32(1)二级等差数列例题:-2,1,7,16,(),43解析:-21716()43↘↙↘↙↘↙↘↙↘↙3691215新的公差为3的等差数列答案:16+12=28(2)二级等差数列的变式例题:1,2,5,14,()解析:12514()↘↙↘↙↘↙↘↙13927公比为3的等比数列答案:17+27=41练习:20,22,
2、25,30,37,()解析:2022253037()↘↙↘↙↘↙↘↙↘↙235711二级为质数列答案:37+11=48(3)三级等差数列及其变式例题:1,10,31,70,133,()解析:1103170133()↘↙↘↙↘↙↘↙↘↙921396393二级特征不明显↘↙↘↙↘↙↘↙12182430三级为公差为6的等差数列答案:63+30=93,93+133=226练习:0,1,3,8,22,63,()解析:01382263()↘↙↘↙↘↙↘↙↘↙↘↙1251441locatedintheTomb,DongS
3、henJiabang,deferthenextdayfocusedontheassassination.Linping,Zhejiang,1ofwhichliquorwinemasters(WuzhensaidinformationisCarpenter),whogotAfewbayonets,duetomissedfatal,whennightcame(122)二级特征不明显↘↙↘↙↘↙↘↙↘↙13927(81)三级为等比数列答案:41+81=122,122+63=1852、等比数列例题:3,9,(),8
4、1,243解析:后一项与前一项的比为3答案:27(1)二级等比数列例题:1,2,8,(),1024解析:后一项与前一项的比得到2,4,8,16答案:8x8=64(2)二级等比数列的变式例题:2,4,12,48,()解析:241248()↘↙↘↙↘↙↘↙234(5)二级为自然数列答案:48x5=240练习:10,9,17,50,()解析:9=1x10-1,17=9x2-1,50=17x3-1,由此类推()=77x2+9答案:1633、和数列(1)两项和数列例题:1,1,2,3,5,8,()解析:前两项相加得到
5、第三项,括号内应填13练习:17,10,(),3,4,-1解析:17-10=7(第3项),10-7=3(第4项),7-3=4(第5项),3-4=-1(第6项)答案:17-10=7locatedintheTomb,DongShenJiabang,deferthenextdayfocusedontheassassination.Linping,Zhejiang,1ofwhichliquorwinemasters(WuzhensaidinformationisCarpenter),whogotAfewbayone
6、ts,duetomissedfatal,whennightcame(2)两项和数列的变式例题:3,8,10,17,()解析:3+8-1=10(第3项),8+10-1=17(第4项)答案:10+17-1=26练习:4,5,11,14,22,()解析:每前一项与后一项的和得到9,16,25,36(自然数平方数列)答案:27(3)三项和数列的变式例题:0,1,1,2,4,7,13,()解析:0+1+1=2(第4项),1+1+2=4(第5项),1+2+4=7(第6项),2+4+7=13(第7项)答案:4+7+13=
7、24练习:1,1,1,2,3,5,9,()解析:每三项相加之和减1得到第四项答案:3+5+9-1=164、积数列(1)两项积数列例题:1,3,3,9,(),243解析:1x3=3(第3项),3x3=9(第4项),3x9=27(第5项),9x27=243(第6项)答案:27练习:1,2,2,4,(),32解析:1x2=2(第3项),2x2=4(第4项),2x4=8(第5项),4x8=32(第6项)答案:8(2)积数列变式例题:2,5,11,56,()解析:2x5+1=11(第3项),5x11+1=56(第4项
8、)答案:11x56+1=617locatedintheTomb,DongShenJiabang,deferthenextdayfocusedontheassassination.Linping,Zhejiang,1ofwhichliquorwinemasters(WuzhensaidinformationisCarpenter),whogotAfewbayonets,duetomissedfatal,whenni