白熊求职数学六大难点数列

解题技巧“等差数列”(arithmeticsequence)，d称为“公差”(commondifference)。对任意正整数iaiai-对任意正整数iai=a1+(i-ai+kai+kda5=a2+3d=a3+2da1…….a2n+1的算数均值为an+1;a1…….a2n的算数均值为 列”(geometricsequence)，q称为“公比”(commonratio)。-对任意正整数n：an=an-对任意正整数naikai*q的ka5a2*qa3*qa1…….a2n+1的几何均值为an+1;a1…….a2nan*an+1.Ifrisaconstantandan=r•nforallpositiveintegersn,forhowmanyvaluesofnisan<100?(1)a50=(2)a100+a105=1.Ifrisaconstantandan=r•nforallpositiveintegersn,forhowmanyvaluesofnisan<100?(1)a50=(2)a100+a105=Step1：判断数列为等差数列,首项为r,公差为rStep2：an100的n的值，只需要求出r即可条件（1）：a50=r•50=500è r=10è an=10n,所以对于n=1,2,3,…9都可满足条件è充分分条件（2）：a100+a105=100r+105r=205r=2050 r=10 an=10nèInthesequenceofnonzeronumberst1,t2,t3,…,tn,…,tn+1=tn/2forpositiveintegersn.Whatisthevalueof

t3=t1-t5=Inthesequenceofnonzeronumberst1,t2,t3,…,tn,…,tn+1=tn/2forpositiveintegersn.Whatisthevalueof

t3=t1-t5=Step1：t11/2Step2：要求t5值，只需要求出t1即可条件（1）：t3=0.5*0.5*t1=1/4è t1=1è tn=(1/2)的(n-1)次方,所以t5=(1/2)的4次方；或者根据等比数列的性质ai+k=ai*q的k次方，t5=t3*0.5*0.5è条件（2）：t1-t5=t1*（1-0.5的四次方）=15/16è t1=1è tn=(1/2)的n次方,所以t5=(1/2)的5次方è充分.Inthesequence1,2,4,8,16,32,…,eachtermafterthefirstistwicethepreviousterm.Whatisthesumofthe16th,17th,and18thtermsintheStepStep1：1,2Step2：要求16,17,18项的和，根据等比数列的.Inthesequence1,2,4,8,16,32,…,eachtermafterthefirstistwicepreviousterm. Whatisthesumofthe16th,17th,and18thtermsinthe.Ifthesequencex1,x2,x3,…,xn,…issuchthatx1=3andxn+1=2xn–1for≥1,thenx20–x19.Ifthesequencex1,x2,x3,…,xn,…issuchthatx1=3andxn+1=2xn–1for≥1,thenx20–x19StepStep1：Theinfinitesequencea1,a2,…,an,…issuchthata1=2,a2=-3,a3=5,a4-1,andan=an-4forn>4.Whatisthesumofthefirst97termsoftheTheinfinitesequencea1,a2,…,an,…issuchthata1=2,a2=-3,a3=5,a4-1,andan=an-4forn>4.Whatisthesumofthefirst97termsoftheStep2：前97项包涵：97/4=24…1，24个完整的循环以及a97a12Inalistofnumbers,thefirstnumberis3,thesecondis4,andeachsubsequentnumberisthesumofalltheprecedingnumbersinthelist.Ifthe20thnumberinthelistisx,whatisthe25thnumberinthelist?Inalistofnumbers,thefirstnumberis3,thesecondis4,andeachsubsequentnumberisthesumofalltheprecedingnumbersinthelist.Ifthe20thnumberinthelistisx