P2.4 - Sequences and series

Sequences, including those given by a formula for the nth term and those generated by a simple relation of the form x = f(x). n + 1 n.

Use sequences, to connect the rule to the data and decision in the question.

This matters because sequences, determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply sequences, to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Sequences, is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Understand and work with The proof of the sum formula should be known. arithmetic sequences and series, including the formula for the nth term and the sum of a finite Σ Understanding of notation will expected. arithmetic series.; the sum of the first n natural numbers.

Use arithmetic sequences and series to connect the rule to the data and decision in the question.

This matters because arithmetic sequences and series determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply arithmetic sequences and series to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Arithmetic sequences and series is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Increasing sequences, decreasing sequences and periodic sequences.

Use increasing sequences, decreasing sequences and periodic to connect the rule to the data and decision in the question.

This matters because increasing sequences, decreasing sequences and periodic determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply increasing sequences, decreasing sequences and periodic to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Increasing sequences, decreasing sequences and periodic is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Understand and work with For example, given the sum of a series students should be geometric sequences and series, able to use logs to find the value of n. including the formulae for the nth The proof of the sum formula for a finite series should be term and the sum of a finite known. geometric series.; the sum to infinity of a convergent geometric series, The sum to infinity may be expressed as S ∞. including the use of |r| < 1.

Use geometric sequences and series to connect the rule to the data and decision in the question.

This matters because geometric sequences and series determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply geometric sequences and series to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Geometric sequences and series is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Expand (a + bx)^n for positive integer n and use the notations n!, binomial coefficients and nCr.

Use binomial expansion for positive integer powers to connect the rule to the data and decision in the question.

This matters because binomial expansion for positive integer powers determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply binomial expansion for positive integer powers to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Binomial expansion for positive integer powers is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.