已知等差数列{an}中,a2+a5+a8=6且a2乘以a5乘以a8=6,

Question

已知等差数列{an}中,a2+a5+a8=6且a2乘以a5乘以a8=6,

Answer 1

a2+a5+a8=6
a2*a5*a8=6
a2+a5+a8=a1+d+a1+4d+a1+7d=6 3a1+12d=6 a1+4d=2 a1=2-4d
a2*a5*a8=(a1+d)(a1+4d)(a1+7d)=6
(2-4d+d)(2-4d+4d)(2-4d+7d)=6
(2-3d)*2*(2+3d)=6 4-9d^2=3 9d^2=1 d=±1/3 d1=1/3 a1=2/3 d2=-1/3 a1=10/3
当 d=1/3 a1=2/3 a2=a1+d=1 a5=a1+4d=2 a8=a1+7d=3
当d=-1/3 a1=10/3 a2=10/3-1/3=3 a5=10/3-4/3=2 a8=10/3-7/3=1