HARD sequence problem help

AP:     a, a+d,  a+2d,  a+3d,  .....

GP      $\frac{1}{a},\; \frac{1}{a+d},\;\frac{1}{a+2d}, \dots$

$r=\frac{T_n}{T_{n-1}}=\frac{1}{a+d}\div\frac{1}{a}=\frac{1}{a+2d}\div\frac{1}{a+d}\;\;etc\\ \frac{a}{a+d}=\frac{a+d}{a+2d}\\ a(a+2d)=(a+d)(a+d)\\ a(a+d)+ad=a(a+d)+d(a+d)\\ ad=ad+d^2\\ d^2=0 \\ d=0\\ $

Hence every term in the AP is 12 and every term in the GP is 1/12

Wow! Thanks melody..

no wonder why i couldnt guess and check, they were all the same!