2022英语周报九年级53答案

18.【试题情境】本题是基础性题目,属于课程学习情境,具体是数学运算学习情境【必备知识】本题考查的知识是“掌握等差数列、等比数列的通项公式与前n项和公式”【关键能力】本题考查逻辑思维能力、运算求解能力【解题思路】(1)a1·a3=a,4n=256设等比数列a,}的公比为q(q>0)2S=b62+b,-2=1时+b2-b1-2=0→b,=2n≥2时b2bn+bn)·(b,+b.>0bn1-1)=02(S.-3n)a错位相减法(2)由(1)→S解:(1)设等比数列|an}的公比为q,q>0,(1分)a12·a3=a1,a8=256,a1q·a1q=a1q,a1q=252(3分)对于2S。=b2+b。-2①当n=1时,21=2b1=b2+b1-2,解得b1=2或b1=-1(舍去)(4分)当n≥2时,2Sn=b21+bn1-2①-②得2b,=b2-b21+b。-b,1,即(b+b,1)·(b。-b1-1)=0b,+bn1>0,b一b。1-1=0,即b-b1=1,(5分)数列|b,是以2为首项,1为公差的等差数列.b,=2+(n-1)×1=n+1.(6分)(2)由(1)可得Sn=n(n+1+2)3n3)·2C(n+1)-1M,=1×22+2×2+3×24+…+(n-1)×2+nx2③则2M,=1×2+2×24+3×23+…+(n-1)×2+n×22④,(10分③-④得-M,=22+23+2++22(1-2”)n×22=-[4+(n-1)×2"2],(11分)∴M,=4+(n-1)×22(12分)解后反思》在解决数列求和问题时,首先需要判断数列通项的特征,然后选择相应的求和方法,如本题中数列{cn}的通项公式是一个等差数列和一个等比数列的通项的积,故采用错位相减法求数列cnl的前n项和
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