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问题:
问题描述:
已知Sn是数列{an}的前n项和,a1=1,a2=2,a3=3,数列{an+an+1+an+2}是公差为2的等差数列,则S25=()
A.232
B.233
C.234
D.235
寇义民回答:
∵数列{an+an+1+an+2}是公差为2的等差数列,
∴an+3-an=(an+1+an+2+an+3)-(an+an+1+an+2)=2,
∴a1,a4,a7,…是首项为1,公差为2的等差数列,
a2,a5,a8,…是首项为2,公差为2的等差数列,
a3,a6,a9,…是首项为3,公差为2的等差数列,
∴S25=(a1+a4+a7+…+a25)+(a2+a5+a8+…+a23)+(a3+a6+a9+…+a24)
=9×1+