数列an满足an=3an-1+3的n次方-1(n大于等于2).又a1=5,则使得(an+b)除以3的n次方为等差数列则b
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数列an满足an=3an-1+3的n次方-1(n大于等于2).又a1=5,则使得(an+b)除以3的n次方为等差数列则b是多少
![数列an满足an=3an-1+3的n次方-1(n大于等于2).又a1=5,则使得(an+b)除以3的n次方为等差数列则b](/uploads/image/z/15946818-42-8.jpg?t=%E6%95%B0%E5%88%97an%E6%BB%A1%E8%B6%B3an%3D3an-1%2B3%E7%9A%84n%E6%AC%A1%E6%96%B9-1%EF%BC%88n%E5%A4%A7%E4%BA%8E%E7%AD%89%E4%BA%8E2%EF%BC%89.%E5%8F%88a1%3D5%2C%E5%88%99%E4%BD%BF%E5%BE%97%28an%2Bb%29%E9%99%A4%E4%BB%A53%E7%9A%84n%E6%AC%A1%E6%96%B9%E4%B8%BA%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%E5%88%99b)
a(n+1)=3a(n) + 3^(n+1) - 1 ,
a(n+1) - 1/2 = 3a(n) + 3^(n+1) - 3/2 = 3[a(n)-1/2] + 3^(n+1),
[a(n+1)-1/2]/3^(n+1) = [a(n)-1/2]/3^(n) + 1,
{[a(n)-1/2]/3^n}是首项为[a(1)-1/2]/3=3/2,公差为1的等差数列.
b=-1/2.
a(n+1) - 1/2 = 3a(n) + 3^(n+1) - 3/2 = 3[a(n)-1/2] + 3^(n+1),
[a(n+1)-1/2]/3^(n+1) = [a(n)-1/2]/3^(n) + 1,
{[a(n)-1/2]/3^n}是首项为[a(1)-1/2]/3=3/2,公差为1的等差数列.
b=-1/2.
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