 # Recurrence relations for SQA Higher Maths 1. Recurrence relationships

A recurrence relationship can be used to generate all the terms of a sequence. It describes each term as a function of the previous term. # 1

The recurrence relationship of a sequence is given by u_(n + 1) = u_n² − 3, where u₁ = 1. Calculate the sum of the first 50 terms.

Generating the first few terms, 1, −2, 1, −2, …
So, the first 50 terms have twenty-five 1 and twenty-five −2.
So, sum = 25(1) + 25(−2) = −25. # 2

The recurrence relationship of a sequence is given by u_(n+1) = 100 − u_n, where u₁ = 18. Calculate the next three terms of the sequence.

u₂ = 100 − 18 = 82.
u₃ = 100 − 82 = 18.
u₄ = 100 − 18 = 82. # 3

Given the recurrence relationship u_(n + 1) = u_n² + 10, fill in the blanks of the sequence.

_____ _____ 42446

42446 = u₂² + 10, so u₂ = √42436 = 206.
206 = u₁² + 10, so u₁ = √196 = 14. # 4

The recurrence relationship of a sequence is given by u_(n+1) = 6u_n², where u₁ = 5. Calculate the next two terms of the sequence.

u₂ = 6(5)² = 150.
u₃ = 6(150)² = 135000. # 5

The recurrence relationship of a sequence is given by u_(n+1) = 11u_n + 8, where u₁ = 3. Calculate the next two terms of the sequence.

u₂ = 11(3) + 8 = 41.
u₃ = 11(41) + 8 = 459. End of page