A sequence is defined by a_n = 5n / (n + 2)!. What is its third term?

1. Substitute n = 3 into the formula, so the numerator is 5(3) = 15. 2. The denominator is (3 + 2)! = 5!. 3. 5! = 5 times 4 times 3 times 2 times 1 = 120. 4. So the third term is 15/120. 5. Dividing numerator and denominator by 15 gives 1/8. 6. The value 5/6 is the first term and 5/12 is the second, so both come from stopping short. 7. The value 1/36 is the fourth term, which is what you get by substituting n = 4 by mistake. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.1 Sequences and Their Notations_