Question

{an}是d不等于0的等差数列,a2^2+a3^2=a4^2+a5^2,S7=7,求an

Answer 1

a4²-a2²=a5²-a3²

(a4+a2)(a4-a2)=(a3-a5)(a3+a5)

因为a4-a2=a5-a3=2d≠0

所以a4+a2=-(a5+a3)

(a1+3d)+(a1+d)=-[(a1+4d)+(a1+2d)]

2a1+4d=-2a1-6d

4a1+10d=0

2a1+5d=0

a1+(a1+5d)=0

a1+a6=0

S7=(a1+a7)*7/2=7

a1+a7=2

相减

a1+a7-a1-a6=2-0

a7-a6=d=2

a1=-5d/2=-5

所以an=-5+2(n-1)

即an=2n-7