Recurrence Relations (Edexcel IAL Maths)

Spec point — 4.1

Recurrence relations

What is a recurrence relation?

• A recurrence relation describes each term in a sequence as a function of the previous term – ie u_n+1 = f(u_n)
• Along with the first term of the sequence, this allows you to generate the sequence term by term

• Both arithmetic sequences and geometric sequences can be defined using recurrence relations

  • Arithmetic can be defined by $u_{n+1}=u_{n}+d,u_{1}=a$
  • Geometric can be defined by $u_{n+1}=u_{n}\times r,u_{1}=a$

• However, you can also define sequences that are neither arithmetic nor geometric

Exam Hint

• For arithmetic or geometric sequences defined by recurrence relations, you can sum the terms using the arithmetic series and geometric series formulae.
• To sum up the terms of other sequences, you may have to think about the series and find a clever trick.

Worked Example