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### Paper 1

NUMBER PATTERNS
Investigate number patterns (including but not limited to those where there is a constant second difference between consecutive terms in a number pattern, and the general term is therefore quadratic) and hence:
(a) make conjectures and generalisations
(b) provide explanations and justifications and attempt to prove conjectures.

Clarification

• Investigate and identify number patterns including but not limited to those with
· constant difference between consecutive terms (linear patterns)
· constant second difference (quadratic patterns)
· constant ratios (exponential patterns)
• Extend the pattern and explain how the terms are generated.
• Determine the general term
• Calculate the term value and the number of terms in a sequence of any pattern.

(a) Identify and solve problems involving number patterns, including but not limited to arithmetic and geometric sequences and series.
(b) Correctly interpret sigma notation.
(c) Prove and correctly select the formula for and calculate the sum of series, including:     Clarification

• Links must be clearly established between patterns done in earlier grades so that for example, learners understand that an arithmetic sequence is a linear pattern and a geometric sequence is an exponential pattern.
• Calculate the term value and the number of terms in a sequence of any pattern.
• Convert fluently between: notation and expanded notation.
• Proofs of the sum of arithmetic and geometric series are examinable.
NOTE:
Recursive formulae are part of number patterns but are tested ONLY in the optional paper 3.