a(n+1)=Sn+2ⁿ
S(n+1)-Sn=Sn+2ⁿ
S(n+1)-2Sn=2ⁿ
等式两边同除以2ⁿ
S(n+1)/2ⁿ-Sn/2^(n-1) =1,为定值.
S1/2^0=a1/1=a
数列{Sn/2^(n-1)}是以a为首项,1为公差的等差数列.
bn=Sn/2^(n-1),数列{bn}是以a为首项,1为公差的等差数列.
bn=a+1×(n-1)=n +a-1
数列{bn}的通项公式为bn=n+a-1.