在等差数列{an}中,(1)若a1+a2+a3+a5+a8+a9+a14=7m,且m=at,则t=______;(2)若a32+2a3a6+a5a7=12,

2025-05-07 05:26:43
推荐回答(1个)
回答1:

(1)等差数列{an}中,
∵a1+a2+a3+a5+a8+a9+a14=7m,且m=at
∴7a1+35d=7m,
∴7(a1+5d)=7m,
∴a6=m,
∴t=6.
(2)∵a4=a3+d,a5=a3+2d,a6=a3+3d,a7=a3+4d,
∵a32+2a3a6+a5a7=12,
a32+2a3(a3+3d)+(a3+2d)(a3+4d)=12
a32+3a3d+2d2=3,
∵a4?a5=(a3+d)(a3+2d)=a32+3a3d+2d2=3.
故答案为:6,3.