Question

在等比数列中，已知a3=3/2，S3=9/2，求a1与q

Answer 1

解：根据已知可得： a1*q�0�5 = 3/2 ① a1+a1*q +a1*q�0�5 = 9/2 ②②÷①，得：（1/q)�0�5+(1/q)+1 = 3∴q = 1 或 q = -1/2此时，a1 = 3/2 或 a1 = 6

Answer 2

S3 = a3 + a1 +a2 = a3/q^2 + a3/q + a3
所以 9/2 = 3/2(1+ 1/q^2+1/q)
解得q=1或q=-1/2
q=1时，a1=3/2;q=-1/2时，a1=6

Answer 3

a3=a1*q^2S3=a1(1-q^3)/(1-q)所以:S3/a3=3=(1-q^3)/q^2(1-q)可解得q=1或-1/2当q=1时，a1=3/2当q=-1/2时，a1=6