Sequences and the nth term

Answer: 3n + 2

1. Common difference = 3, so the rule starts 3n
2. n = 1 gives 3, but the first term is 5, so add 2

• A. 3n + 2 — Correct: the common difference is 3, and when n = 1 the rule gives 5.
• B. 3n − 2 — The difference is right, but n = 1 gives 1, not 5. Always test your rule on the first term.
• C. 5n + 3 — The first term was used as the coefficient. The coefficient is the difference between terms, not the first term.
• D. n + 3 — These terms grow by 3 each time, not by 1.

Examiner technique: One mark, five seconds of checking: substitute n = 1 and n = 2 into your own rule. It is the cheapest verification in the whole paper.

Answer: (a) 77 (b) No, because 4n − 3 = 100 gives n = 25.75, and n must be a whole number.

1. (a) 4 × 20 − 3 = 77
2. (b) Set 4n − 3 = 100
3. Solving: n = 25.75, which is not a whole number, so 100 is not in the sequence

Examiner technique: Part (b) is an analysis mark, not a guess. Say what you solved and what the non-integer result means — the meaning is the mark.