可能是等差数列、等比数列、其它数列,应说明.
s5=8
s10=8+56=64
s15=?
1.等差数列：
设an=a+(n-1)d
sn=na+(1/2)n(n+1)d
s5=5a+15d=8
s10=10a+55d=8+56=64
a=-104/25
d=48/25
s15=15a+120d=168
a11+a12+a13+a14+a15=s15-s10=168-64=104;
2.等比数列：
设an=aq^(n-1)
sn=a(1-q^n)/(1-q)
s5=a(1-q^5)/(1-q)=8
s10=a(1-q^10)/(1-q)=56+8=64
两式相除:
1+q^5=64/8=8
q^5=7
1-q=a(1-q^5)/8
s15=a(1-q^15)/(1-q)
=a(1-q^15)/[a(1-q^5)/8]
=8(1-q^15)/(1-q^5)
=8(1-7^3)/(1-7)
=456
a11+a12+a13+a14+a15
=s15-s10
=456-64
=392
3.其它数列 :
无法算.