The nth term of a quadratic sequence
The Maths Habit
Find the nth term of 2, 7, 12, 17, …
5n − 3Find the nth term of −4, −1, 2, 5, …
3n − 7The nth term of a sequence is 6n + 5. Is 80 in the sequence?
No: n = 12.5
Sam says 2, 5, 10, 17, 26 is not a sequence, because it does not go up by the same each time. Is Sam right?
No: it goes up by 3, 5, 7, 9, which is a rule too
- Second difference
- The difference between the differences. In a quadratic sequence it is always the same.
Find the nth term of 6, 9, 14, 21, 30
| sequence | 6 | 9 | 14 | 21 | 30 |
|---|---|---|---|---|---|
| the n2 part | 1 | 4 | 9 | 16 | 25 |
| what is left | 5 | 5 | 5 | 5 | 5 |
Find the nth term of 5, 11, 21, 35, 53
| sequence | 5 | 11 | 21 | 35 | 53 |
|---|---|---|---|---|---|
| the n2 part | 2 | 8 | 18 | 32 | 50 |
| what is left | 3 | 3 | 3 | 3 | 3 |
Find the nth term of 6, 9, 14, 21, 30
| sequence | 6 | 9 | 14 | 21 | 30 |
|---|---|---|---|---|---|
| the n2 part | 1 | 4 | 9 | 16 | 25 |
| what is left | 5 | 5 | 5 | 5 | 5 |
Find the nth term of 3, 8, 15, 24, 35
| sequence | 3 | 8 | 15 | 24 | 35 |
|---|---|---|---|---|---|
| the n2 part | 1 | 4 | 9 | 16 | 25 |
| what is left | 2 | 4 | 6 | 8 | 10 |
Find the nth term of 6, 9, 14, 21, 30
| sequence | 6 | 9 | 14 | 21 | 30 |
|---|---|---|---|---|---|
| the n2 part | 1 | 4 | 9 | 16 | 25 |
| what is left | 5 | 5 | 5 | 5 | 5 |
Find the nth term of 5, 11, 21, 35, 53
| sequence | 5 | 11 | 21 | 35 | 53 |
|---|---|---|---|---|---|
| the n2 part | 2 | 8 | 18 | 32 | 50 |
| what is left | 3 | 3 | 3 | 3 | 3 |
Find the nth term of 6, 9, 14, 21, 30
| sequence | 6 | 9 | 14 | 21 | 30 |
|---|---|---|---|---|---|
| the n2 part | 1 | 4 | 9 | 16 | 25 |
| what is left | 5 | 5 | 5 | 5 | 5 |
Find the nth term of 6, 11, 18, 27, 38
| sequence | 6 | 11 | 18 | 27 | 38 |
|---|---|---|---|---|---|
| the n2 part | 1 | 4 | 9 | 16 | 25 |
| what is left | 5 | 7 | 9 | 11 | 13 |
Find the nth term of 6, 9, 14, 21, 30
| sequence | 6 | 9 | 14 | 21 | 30 |
|---|---|---|---|---|---|
| the n2 part | 1 | 4 | 9 | 16 | 25 |
| what is left | 5 | 5 | 5 | 5 | 5 |
Find the nth term of 4, 14, 30, 52, 80
| sequence | 4 | 14 | 30 | 52 | 80 |
|---|---|---|---|---|---|
| the n2 part | 3 | 12 | 27 | 48 | 75 |
| what is left | 1 | 2 | 3 | 4 | 5 |
Answer sheet
The nth term of a sequence is n2 + 3n. Which term is 70?
The 7thA pattern uses 1, 3, 6, 10, 15 dots. Find the nth term.
12n2 + 12n
Find the nth term of 2, 11, 26, 47, 74, …
3n2 − 1Find the nth term of 4, 11, 20, 31, 44, …
n2 + 4n − 1Ella says the nth term of 5, 8, 13, 20, 29, … is 2n2 + 3. Is she right? Explain how you know.
No: it is n2 + 4