n≥2时,
an=3ⁿ+2a(n-1)
等式两边同除以2ⁿ
an/2ⁿ=(3/2)ⁿ +a(n-1)/2^(n-1)
an/2ⁿ -a(n-1)/2^(n-1)=(3/2)ⁿ
a(n-1)/2^(n-1) -a(n-2)/2^(n-2)=(3/2)^(n-1)
…………
a2/2²-a1/2=(3/2)²
累加
an/2ⁿ- a1/2=(3/2)²+(3/2)³+...+(3/2)ⁿ
an/2ⁿ=a1/2 +(3/2)²+(3/2)³+...+(3/2)ⁿ
=1/2+(3/2)²+(3/2)³+...+(3/2)ⁿ
=(3/2)+(3/2)²+(3/2)³+...+(3/2)ⁿ -1
=(3/2)×[(3/2)ⁿ-1]/(3/2-1) -1
=3^(n+1)/2ⁿ -4
an=3^(n+1) -4×2ⁿ=3^(n+1)-2^(n+2)
n=1时,a1=3²-2³=1,同样满足通项公式
数列{an}的通项公式为an=3^(n+1) -2^(n+2)