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