在等差数列中,若a1的二次方+a2的二次方等于a3的二次方+a4的二次方,S5=5,则a7

Question

在等差数列中,若a1的二次方+a2的二次方等于a3的二次方+a4的二次方,S5=5,则a7

Answer 1

a=a1+(n-1)d
(a1)^2+(a2)^2 = (a3)^2 +(a4)^2
(a1)^2+(a1+d)^2 = (a1+2d)^2 +(a1+3d)^2
2a1d+d^2 = 4a1d+4d^2 + 6a1d +9d^2
8a1d+ 12d^2=0
d(2a1+3d)=0
d=0 or d = -2a1/3
S5= (a1+2d)5= 5
a1+2d=1
case1:d=0
a1= 1 => a7 = 1
case2:d=-2a1/3
a1=-3
d = 2
a7 = a1+6d = -3+2(2) =1