質問: (5 + 3^n*(4*n - 5))/2 を解にもつ漸化式を作成願います。
回答: a[n]=(5+3^n(4n-5))/2 a[n+1]-a[n] =[5+3^(n+1){4(n+1)-5}]/2-{5+3^n(4n-5)}/2 ={3^(n+1)(4n+4-5)-3^n(4n-5)}/2 =(3^n){3(4n-1)-4n+5}/2 =(3^n)(12n-3-4n+5)/2 =(3^n)(8n+2)/2 =(3^n)(4n+1) a[n+1]-a[n]=(3^n)(4n+1) ∴ a[n+1]=a[n]+(3^n)(4n+1)