The fifth excited state corresponds to the principal quantum number n₂ = 6. The second excited state corresponds to n₁ = 3. The number of possible spectral lines is given by the formula (n₂ - n₁)(n₂ - n₁ + 1) / 2 = (6 - 3)(6 - 3 + 1) / 2 = (3 * 4) / 2 = 6. [cite: 263, 264, 270, 271, 272, 273]