公差不为零 的等差数列的2,4,7,项成等比数列其公比是?
问题描述:
公差不为零 的等差数列的2,4,7,项成等比数列其公比是?
答
设等差数列公差为d,∴a2=a1+d(1)a4=a1+3d(2)a7=a1+6d(3)由a2:a4=a4:a7,(a1+d):(a1+3d)=(a1+3d):(a1+6d),a1²+7a1d+6d²=a1²+6a1d+9d²,a1d=3d²,∴a1=3d,将a1=3d代入a2:a4=...