a(n+1)=3an+2ⁿ+3n²-1
a(n+1)+2^(n+1)+(3/2)(n+1)² +(3/2)(n+1)+1=3an+3×2ⁿ+(9/2)n²+(9/2)n+3
[a(n+1)+2^(n+1)+(3/2)(n+1)² +(3/2)(n+1)+1]/[an+2ⁿ+(3/2)n²+(3/2)n+1]=3,为定值.
a1+2+ 3/2 +3/2 +1=1+2 +3/2 +3/2 +1=7
数列{an+2ⁿ+(3/2)n²+(3/2)n+1}是以7为首项,3为公比的等比数列.
an+2ⁿ+(3/2)n²+(3/2)n+1=7×3^(n-1)
an=7×3^(n-1) -2ⁿ -(3/2)n² -(3/2)n-1