已知等差数列an的公差d大于0,且a3,a5是方程x^2-14x+45=0的两根
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已知等差数列an的公差d大于0,且a3,a5是方程x^2-14x+45=0的两根
求数列an的通项公式
记bn=2的an次方+你,求数列bn的前n项和Sn
an =a1+(n-1)d
a3+a5= 14
2a1+6d=14
a1+3d=7 (1)
a3.a5=45
(a1+2d)(a1+4d)=45
(7-d)(7+d)=45
d^2=4
d=2
from (1),a1=1
an = 1+2(n-1) = 2n-1
bn=2^(an) +n
= 2^(2n-1) +n
Sn = b1+b2+...+bn
= 2( 2^(2n) -1) /(4-1) + n(n+1)/2
=(2/3)( 2^(2n) -1) + n(n+1)/2
a3+a5= 14
2a1+6d=14
a1+3d=7 (1)
a3.a5=45
(a1+2d)(a1+4d)=45
(7-d)(7+d)=45
d^2=4
d=2
from (1),a1=1
an = 1+2(n-1) = 2n-1
bn=2^(an) +n
= 2^(2n-1) +n
Sn = b1+b2+...+bn
= 2( 2^(2n) -1) /(4-1) + n(n+1)/2
=(2/3)( 2^(2n) -1) + n(n+1)/2
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