# The nth term (starter) If each term adds the same number `d`, it is an **arithmetic** pattern. nth term (starter version): `first term + (n − 1) × step` Example: 5, 8, 11, 14… First = 5, step = 3 nth term = `5 + (n − 1)×3 = 3n + 2` Check: n=1 → 3+2=5 ✓ · n=2 → 6+2=8 ✓ ## You do not need the name “arithmetic sequence” in Class 6 to use this. You only need: *start, step, position.* Next stop after this path: more equations, and later graphs. You already have the core idea — **letters hold numbers, and = is a balance.** ## Start, step, seat You only need three words: - **Start** — the first term - **Step** — what you add each time - **Seat** — n, the position ``` term(n) = start + (n − 1) × step ``` Why n − 1? From your own seat back to the first seat there are n − 1 jumps, not n. ### Check pair (never skip) - n = 1 must return the start - n = 2 must return start + step If either fails, the algebra of tidying start + (n−1)d went wrong. Redo that line. ### You already own the whole starter path Letters hold numbers. Equals is a balance. Substitution checks truth. The nth term is those three ideas wearing a sequence costume.