AK = a 1+(k- 1)d =(k+8)d

a2k = a 1+(2k- 1)d =(2k+8)d

Ak is the equal ratio median of a 1 and a2k,

ak^2=a 1*a2k

(k+8) 2d 2 = 9d * (2k+8) d d is not 0.

k^2+ 16k+64= 18k+72

k^2-2k-8=0

K=4 or k=-2

K is a positive integer, so k=4.