等比数列an中,已知a1+a2+a3=4.a2+a3+a4=-2.则a3+a4+a5+a6+a7+a8=?

2024-11-22 05:04:18
推荐回答(1个)
回答1:

S3=4=a1(q^3-1)/(q-1)S4-a1=-2=a1(q^4-1)/(q-1) -a1[(q^4-1)/(q-1) -1]/(q^3-1)/(q-1)=-1/2[(q^4-q)/(q^3-1)]=-1/2q=-1/渗梁2a1=4(1+1/2)/(1+1/8)=6/(9/8)=16/3a3+a4+...+a8=S8-S2=a1(1-q^8)/(1-q) -a1(1-q^2)/(1-q)=a1(q^2-q^8)/(1-q)=a1q^2(1-q^6)/让喊蔽(1-q)=(16/3)(1/4)(1-1/64)/(1+1/2)=(4/3)(63/64)(2/坦州3)=7/8