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# 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_nĀ² ā 3, where uā = 1. Calculate the sum of the first 50 terms.

Generating the first few terms, 1, ā2, 1, ā2, ā¦
So, the first 50 terms have twenty-five 1 and twenty-five ā2.
So, sum = 25(1) + 25(ā2) = ā25.

# 2

The recurrence relationship of a sequence is given by u_(n+1) = 100 ā u_n, where uā = 18. Calculate the next three terms of the sequence.

uā = 100 ā 18 = 82.
uā = 100 ā 82 = 18.
uā = 100 ā 18 = 82.

# 3

Given the recurrence relationship u_(n + 1) = u_nĀ² + 10, fill in the blanks of the sequence.

_____ _____ 42446

42446 = uāĀ² + 10, so uā = ā42436 = 206.
206 = uāĀ² + 10, so uā = ā196 = 14.

# 4

The recurrence relationship of a sequence is given by u_(n+1) = 6u_nĀ², where uā = 5. Calculate the next two terms of the sequence.

uā = 6(5)Ā² = 150.
uā = 6(150)Ā² = 135000.

# 5

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

uā = 11(3) + 8 = 41.
uā = 11(41) + 8 = 459.

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