ย 

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_nยฒ โˆ’ 3, where uโ‚ = 1. Calculate the sum of the first 50 terms.

Generating the first few terms, 1, โˆ’2, 1, โˆ’2, โ€ฆ
So, the first 50 terms have twenty-five 1 and twenty-five โˆ’2.
So, sum = 25(1) + 25(โˆ’2) = โˆ’25.

The recurrence relationship of a sequence is given by u_(n + 1) = u_nยฒ โˆ’ 3, where uโ‚ = 1. Calculate the sum of the first 50 terms.

2

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

uโ‚‚ = 100 โˆ’ 18 = 82.
uโ‚ƒ = 100 โˆ’ 82 = 18.
uโ‚„ = 100 โˆ’ 18 = 82.

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

3

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

_____ _____ 42446

42446 = uโ‚‚ยฒ + 10, so uโ‚‚ = โˆš42436 = 206.
206 = uโ‚ยฒ + 10, so uโ‚ = โˆš196 = 14.

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

_____ _____ 42446

4

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

uโ‚‚ = 6(5)ยฒ = 150.
uโ‚ƒ = 6(150)ยฒ = 135000.

The recurrence relationship of a sequence is given by u_(n+1) = 6u_nยฒ, where uโ‚ = 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 uโ‚ = 3. Calculate the next two terms of the sequence.

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

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

End of page

ย