GCSE Maths Sequences and nth Term: lesson and practice questions

By the end of this chapter you will be able to

• Continue a sequence using a term-to-term rule, and describe the rule in words
• Generate terms from a position-to-term rule (an nth-term formula)
• Continue and describe patterns made from matchsticks, tiles and dots
• Find the nth term of an arithmetic (linear) sequence using the common difference
• Decide whether a number is a term of a sequence, and find the first term above or below a value
• Recognise square, cube, triangular, Fibonacci-type and geometric sequences

You should already know

• Adding, subtracting, multiplying and dividing whole numbers, decimals and negative numbers (Chapter 1)
• Square numbers, cube numbers and index notation (Chapter 2)
• The order of operations, BIDMAS (Chapter 1)
• Collecting terms and using letters in algebra (Chapter 7)

Where this leads

• Straight-line graphs: the nth term is like y = mx + c (Chapter 12)
• Quadratic graphs, which have the same shape as quadratic sequences (Chapter 13)
• Solving quadratic equations (Chapter 14)
• Compound interest and growth are geometric sequences (Chapters 5 and 25)