设数列{an}是公比为整数的等比数列,且a1+a4=18,a2+a3=12。求

2025-06-24 04:22:45
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回答1:

a1(1+q^3)=18
a1q(1+q)=12
(1+q^3)/q(1+q)=3/2
(1-q+q²)/q=3/2
2q²-5q+2=0
q=2或q=1/2(舍去)
a1=2
an=2*2^(n-1)=2^n

S8=a1(1-q^8)/(1-q)
=2×(1-2^8)/(1-2)
=2^9-2
=510