www.1862.net > 已知A3=3/2,S3=9/2.求A1与q.

已知A3=3/2,S3=9/2.求A1与q.

依题意, 当q=1,很明显,a1 = a2 =a3 = 3/2,s3=9/2, 满足要求; 当q 不等于1 时, a3= a1*q^2 = 3/2 , s3 = a1*(1-q^3)/(1-q) = 9/2; 两式相除消掉a1 ,得到 q^2(1-q)/(1-q^3)=q^2(1-q)/(1-q)(1+q+q^2)=q^2/(1+q+q^2)1/3,则 化简后为 2q^2-q-1=0,...

∵a3=a1q=3/2 S3=a1(1一q^3)/(1一q)解一下

最佳答案 a3=a1q^2=3/2 S3=a1+a1q+a1q^2=9/2 q^2/(1+q+q^2)=1/3 2q^2-q-1=0 (2q+1)(q-1)=0 q=-1/2, a1=(3/2)/q^2=6 或:q=1, a1=3/2

s3=a3(1/q²+1/q+1)=3/2(1+q+q²)/q²=9/2 得:1+q+q²=3q² 2q²-q-1=0 (2q+1)(q-1)=0 q=-1/2, 1 当q=-1/2时, a1=a3/q²=3/2/(-1/2)²=6 当q=1时, a1=a3=3/2

a1+a1q+a1q∧2=9/2 a1q∧2=3/2 解方程得q=-1/2(q'=1不满足) a1=6

解: S3=9/2 a3/q²+a3/q+a3=9/2 a3=3/2代入,整理,得 2q²-q-1=0 (q-1)(2q+1)=0 q=1或q=-½ q=1时,a1=a3=3/2 q=-½时,a1=a3/q²=(3/2)/(-½)²=6

q等于负二分之一,a等于六

a3/q² + a3/q + a3 = S3 3/2(1/q² + 1/q + 1) = 9/2 1/q² + 1/q + 1 = 3 1/q² + 1/q - 2 = 0 (1/q - 1)(1/q + 2) = 0 q = 1 或 q = -1/2 当 q = 1 时 ,a1 = 3/2 当 q = -1/2 时 ,a1 = 6

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