已知等差数列an满足:a5=9,a2+a6=14.1.求an通项公式.2.若bn=an+2^an,求数列bn的前n项和Sn

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已知等差数列an满足:a5=9,a2+a6=14.1.求an通项公式.2.若bn=an+2^an,求数列bn的前n项和Sn
已知等差数列an满足:a5=9,a2+a6=14.1.求an通项公式.2.若bn=an+2^an,求数列bn的前n项和Sn

已知等差数列an满足:a5=9,a2+a6=14.1.求an通项公式.2.若bn=an+2^an,求数列bn的前n项和Sn
1.由a4+d=9,2a4=14得a4=7,d=2,∴an=a4+(n-4)d=2n-1
2.bn=2n-1+2^(2n-1)=2n-1+0.5*4^n
∴Sn=1+3+...+(2n-1)+0.5(4+4^2+...+4^n)
=n^2+2(4^n-1)/3

an=2n-1
bn=6n-3
Sn=n(b1+bn)/2

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