IGCSE Maths Sequences topical questions

A sequence starts 7, 10, 13, 16, ….

1. (a)Write down the next two terms.[1]
2. (b)State the term-to-term rule.[1]
3. (c)Find the 10th term.[1]

Find the nth term of each sequence.

1. (a)4, 7, 10, 13, …[2]
2. (b)20, 17, 14, 11, …[2]

A sequence has nth term 6n + 1.

1. (a)Write down the first three terms.[2]
2. (b)Which term of the sequence equals 43?[2]

A sequence starts 5, 12, 19, 26, ….

1. (a)Write down the term-to-term rule.[1]
2. (b)Write down the next two terms.[1]
3. (c)Find an expression for the term in position n.[2]
4. (d)Is 111 a term of this sequence? Show how you decide.[1]

A sequence has nth term 8 − 3n.

1. (a)Write down the first three terms.[2]
2. (b)Which term of the sequence equals −13?[2]
3. (c)Describe what happens to the terms as n increases.[1]

A quadratic sequence starts 2, 9, 20, 35, ….

1. (a)Show that the nth term is 2n² + n − 1.[3]
2. (b)Find the 10th term.[1]

A geometric sequence starts 3, 6, 12, 24, …. (Extended)

1. (a)Write down the next two terms.[1]
2. (b)Find the nth term.[2]
3. (c)Which is the first term greater than 1000?[1]

Cubic sequences.

1. (a)Show that the sequence 1, 8, 27, 64, … has nth term n³.[1]
2. (b)Find the nth term of 2, 16, 54, 128, ….[2]
3. (c)Find the 5th term of the sequence in part (b).[1]

A sequence starts 4, 13, 28, 49, ….

1. (a)Find the first differences of the sequence.[1]
2. (b)Find the second difference.[1]
3. (c)Find a formula for the nth term of the sequence.[3]

An investment of 200 doubles in value every 5 years. (Extended)

1. (a)Find its value after 15 years.[2]
2. (b)Write an expression for its value after n five-year periods.[2]
3. (c)After how many years does the value first exceed 10 000? Show your working.[2]

A fence is built from square panels. Pattern 1 uses 4 rods, pattern 2 uses 7 rods, pattern 3 uses 10 rods. (Extended)

1. (a)Complete the table for patterns 4 and 5.[2]
2. (b)Find an expression for the number of rods in pattern n.[2]
3. (c)Explain why no pattern uses exactly 50 rods.[1]

A sequence starts 1, 10, 25, 46, 73, ….

1. (a)Find the second difference and explain what it tells you.[1]
2. (b)Show that the nth term is 3n² − 2.[3]
3. (c)Determine whether 122 is a term of the sequence.[1]

A sequence has nth term n² − 8n + 3. (Extended)

1. (a)Write down the values of the first four terms.[2]
2. (b)Write down the smallest term of the sequence and the value of n that gives it.[2]
3. (c)Show that 0 is not a term of this sequence.[3]

A geometric sequence starts 162, 54, 18, 6, …. (Extended)

1. (a)Write down the common ratio.[1]
2. (b)Write down the next two terms.[1]
3. (c)Find an expression for the term in position n.[3]
4. (d)Which term of the sequence equals 2/9?[2]