Free Sequences questions for IGCSE Mathematics (0580), part of Algebra & graphs. Each question has the answer and the marking points an examiner would look for.
Generate a full Sequences worksheet →All Algebra & graphs questionsFind the nth term of the sequence
6, 10, 18, 30, 46, …
Which term of the sequence is equal to 150?
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 2n2 − 2n + 6 second differences 4, so 2n2 M1 remaining sequence linear: −2n + 6 M1 2n2 − 2n + 6 A1 | 3 |
| (b) | the 9th term 2n2 − 2n + 6 = 150 solved M1 9 A1 | 2 |
Here are the first four terms of a sequence.
9, 11, 13, 15
Find the nth term.
Find the 20th term.
Show that 30 is not a term in the sequence.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 2n + 7 2n B1 2n + 7 B1 | 2 |
| (b) | 47 47 B1 | 1 |
| (c) | non-integer n solves nth term = value giving non-integer n B1 | 1 |
The first term of a geometric sequence is 2 and the common ratio is 3.
Find the nth term.
Find the first term that is greater than 1000.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 2 × 3n − 1 2 × 3n − 1 B1 | 1 |
| (b) | 1458 repeated multiplication or trial M1 1458 A1 | 2 |
The first five terms of a sequence are
6, 13, 24, 39, 58, …
Find an expression, in terms of n, for the nth term.
Show that 468 is a term of the sequence and find its position.
Find the first term of the sequence that is greater than 1413.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 2n2 + n + 3 second difference 4 M1 2n2 used M1 2n2 + n + 3 A1 | 3 |
| (b) | n = 15 2n2 + n − 465 = 0 M1 solve (factorise or formula) M1 n = 15 (positive integer) A1 | 3 |
| (c) | 1488 (the 27th term) trial or solving the inequality M1 1488 A1 | 2 |
Find the nth term of the sequence
1, −2, −3, −2, 1, …
Which term of the sequence is equal to 141?
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | n2 − 6n + 6 second differences 2, so n2 M1 remaining sequence linear: −6n + 6 M1 n2 − 6n + 6 A1 | 3 |
| (b) | the 15th term n2 − 6n + 6 = 141 solved M1 15 A1 | 2 |
The nth term of sequence P is 6n − 5.
The nth term of sequence Q is 67 − 3n.
The kth term of P is equal to the kth term of Q.
Find k and the value of this term.
| Part | Answer and marking points | Marks |
|---|---|---|
| k = 8, term = 43 6k − 5 = 67 − 3k M1 k = 8 A1 43 A1 | 3 |
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Meet Riyaz →Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in