已知数列{an}是等差数列,且a1=2,a1+a2+a3=9.(1)求数列{an}的通项公式;(2)令bn=an2an求数列{bn}前

2025-05-14 10:21:45
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(1)数列{an}是等差数列,且a1=2,a1+a2+a3=9,设出公差为d,
∴a1+a1+d+a1+2d=9,∴a1+d=3,可得2+d=3,解得d=1,
∴an=a1+(n-1)d=2+(n-1)×1=n+1;
(2)bn=an2an=(n+1)?2n+1,设其前n项和为Sn
∴Sn=2?22+3?23+…+(n+1)?2n+1
2Sn=2?23+3?24+…+(n+1)?2n+2
①-②可得-Sn=2?22+23+…+2n+1-(n+1)?2n+2
∴Sn=n?2n+2