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?
题目
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?
答案
∵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
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