在等差数列An中,若An>0,公差d>0,则有A4*A6>A3*A7,求问A4*A6>A3*A7是怎么得出来的?
问题描述:
在等差数列An中,若An>0,公差d>0,则有A4*A6>A3*A7,求问A4*A6>A3*A7是怎么得出来的?
答
a4=a1+3d,a6=a1+5d,a3=a1+2d,a7=a1+6d
∴a4×a6=a1²+8da1+15d²,a3×a7=a1²+8da1+12d²
又∵an>0且d>0
∴可得a4×a6>a3×a7
答
∵在等差数列中,A4=A1+3d A6=A1+5d A3=A1+2d A7=A1+6d
∴A4*A6=(A1+3d)(A1+5d)=A1²+8A1d+15d²
A3*A7=(A1+2d)(A1+6d)=A1²+8A1d+12d²
∴A4*A6-A3*A7
=3d²>0
∴A4*A6>A3*A7