设数列{an}满足an=2an-1+n 若{an}是等差数列,求{an}通项公式

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设数列{an}满足an=2an-1+n 若{an}是等差数列,求{an}通项公式

设数列{an}满足an=2an-1+n 若{an}是等差数列,求{an}通项公式
设数列{an}满足an=2an-1+n 若{an}是等差数列,求{an}通项公式

设数列{an}满足an=2an-1+n 若{an}是等差数列,求{an}通项公式
∵{an}是等差数列 ∴an=a1+(n-1)d
∵an=2an﹣1+n ∴a1+(n-1)d=2a1+2(n-2)d+n
∴a1+(n-3)d+n=0 ∴an﹣2=﹣n
∴an=﹣(n+2)

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