BG-MO 1973 Problem 2

Let the numbers $a_1,a_2,a_3,a_4$ form an arithmetic progression with difference $d\ne0$ . Prove that there are no exists geometric progressions $b_1,b_2,b_3,b_4$ and $c_1,c_2,c_3,c_4$ such that: $$a_1=b_1+c_1,a_2=b_2+c_2,a_3=b_3+c_3,a_4=b_4+c_4.$$