PEAZIT Aha card
Go straight to resources ↓Arithmetic sequences: add the same amount each time
From the first to the nth term, take n − 1 steps. Each adds the same difference d: a_n = a_1 + (n − 1)d.
| Expression | Meaning |
|---|---|
| a_1 = 4; d = 3 | Neighbouring terms differ by 3. |
| a_5 = 4 + (5 − 1) · 3 | Four steps lead to the fifth term. |
| a_5 = 16 | 4 + 12 = 16. |
One worked example
- a_1 = 4; d = 3Neighbouring terms differ by 3.
- a_5 = 4 + (5 − 1) · 3Four steps lead to the fifth term.
- a_5 = 164 + 12 = 16.
Watch out: The difference may be negative or zero. One matching pair alone does not establish an arithmetic sequence.
Goal, prerequisites and card origin
What you will learn: Find the nth term of a sequence with constant difference.
What you need first: Multiplication and term positions.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
Show connections
From the first to the nth term, take n − 1 steps. Each adds the same difference d: a_n = a_1 + (n − 1)d.