If a₁ = 4 and aₙ₊₁ = aₙ + 2aₙ, what is a₄?
First simplify the recurrence using like terms. Since aₙ₊₁ = aₙ + 2aₙ, the right side is 3aₙ, so the rule becomes aₙ₊₁ = 3aₙ. This means every term is three times the preceding term. Starting from a₁ = 4, calculate a₂ = 3 × 4 = 12, then a₃ = 3 × 12 = 36, and finally a₄ = 3 × 36 = 108. Therefore option C is correct. The sequence is 4, 12, 36, 108. The other choices do not result from repeated multiplication by 3; they could arise from treating the expression as an addition rule, multiplying by an incorrect factor, or making an error in one of the intermediate terms. Combining like terms is the key step.