{an}等差数列an大于0.a2a4+2a3a5+a4a6=25求a3+a5
问题描述:
{an}等差数列an大于0.a2a4+2a3a5+a4a6=25求a3+a5
答
a2=a3-a1a4=a3+a1a4=a5+a1a6=a5+a1∴a2a4+2a3a5+a4a6=(a3-a1)(a3+a1)+2a3a5+(a5-a1)(a5+a1)=a3²-a1²+2a3a5+a5²-a1²=(a3+a5)²-2a1²∴(a3+a5)²-2a1²=25