Choice D is the answer because it is the only answer choice that has a_1 = 5 as the proper first term.
The original equation a_n = 5*(-1/8)^(n-1) is in the form a_n = a_1*(r)^(n-1). Match up terms to find that a_1 = 5 and r = -1/8.
Note: the recursive step shown in choice D basically says "to get the nth term, multiply the previous (n-1)st term by (-1/8)"