Question

数列问题17题，谢谢了

Answer 1

1）a5,a3,a4成等差数列郑饥扰，有2a3=a4+a5，即2a1*q^2=a1*q^3+a1*q^4
有2=q+q^2；q=1或-2
又a4=a1-9,所肢滚以q=-2
a4-a1=a1(q^3-1)=-9*a1=-9,a1=1
an=a1*q^(n-1)=(-2)^(n-1)
2)证明
S(k)=(1-(-2)^k)/(1-(-2))=(1-(-2)^k)/3
S(k+2)=(1-(-2)^(k+2))/喊旦3
S(k+1)=(1-(-2)^(k+1))/3
S(k+1)+S(k+2)=(1-(-2)^(k+2)+(1-(-2)^(k+1))/3=(2+(-2)^(k+1))/3
=(2-2*(-2)^k)/3=2*(1-(-2)^k)/3=2*S(k)
所以Sk+2,Sk,Sk+1成等差数列