1 设等差数列an的公差为正数,若a1+a2+a3=15,a1*a2*a3=80,则a11+a12+a13=
2个回答
1,
a(n)=a+(n-1)d,
15=a(1)+a(2)+a(3)=3a+3d,5=a+d.
80=a(1)a(2)a(3)=a(a+d)(a+2d)=(a+d-d)*5(a+d+d)=(5-d)*5(5+d),16=25-d^2,d^2=9,d=3.
a=5-d=2.
a(11)+a(12)+a(13)=a+10d+a+11d+a+12d=3a+33d=3*2+33*3=105.
2,
a(1)=1,a(2)-a(1)=1/3,
a(n+1)-a(n)=[a(2)-a(1)](1/3)^(n-1)=(1/3)^n,
a(n)-a(n-1)=(1/3)^(n-1),
...
a(2)-a(1)=(1/3)^(1),
a(n+1)-a(1)=(1/3)^1+(1/3)^2+...+(1/3)^n=(1/3)[1-(1/3)^n]/[1-1/3]=(1/2)[1-1/3^n],
a(n)-a(1)=(1/2)[1-1/3^(n-1)],
a(n)=1+(1/2)[1-1/3^(n-1)],
3,
0=sin(2A),A=90（度）.
C=90-B=90-60=30（度）.
c=b*tan(C)=2tan(30)=2*3^(1/2)/3
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