Explanation

3ˣ + 3ˣ⁺¹ + 3ˣ⁺² = 3ˣ(1 + 3 + 9) = 13·3ˣ. The question asks for the largest listed option dividing this for every positive integer x. For x = 1 the value is 39, which is not divisible by 117, so 117 cannot be the answer. The value 39 = 3 × 13 always divides 13·3ˣ and is the largest listed option that does. Note (key disputed): one published answer key lists (d) 117, but 117 fails at x = 1, so the stored key (c) 39 is retained.