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Recurrence relations for SQA Higher Maths

Recurrence relations

This page covers the following topics:

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.

Recurrence relationships

1

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

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

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

2

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

uā‚‚ = 100 āˆ’ 18 = 82.
uā‚ƒ = 100 āˆ’ 82 = 18.
uā‚„ = 100 āˆ’ 18 = 82.

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

3

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

_____ _____ 42446

42446 = u₂² + 10, so uā‚‚ = √42436 = 206.
206 = u₁² + 10, so u₁ = √196 = 14.

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

_____ _____ 42446

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.

uā‚‚ = 6(5)² = 150.
uā‚ƒ = 6(150)² = 135000.

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.

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.

uā‚‚ = 11(3) + 8 = 41.
uā‚ƒ = 11(41) + 8 = 459.

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.

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