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LearnAQA7357First teaching 2017Paper 1 · PureSequences and series

Paper 1 · Module

Sequences and series

5 subtopics≈ 210 min in total

Start the module: Binomial expansion Open graphing calculator

Binomial expansion
How to expand $(a+b)^n$ without multiplying out $n$ brackets, using Pascal's triangle or $\binom{n}{r}$ , and how to pick out one term, such as the coefficient of $x^3$ or the term independent of $x$ .
≈ 45 min
Arithmetic progressions
Sequences that go up (or down) by the same amount each time: the $n$ th term, the sum of the first $n$ terms and why it works, and how to find unknowns from given terms or sums.
≈ 40 min
Geometric progressions
Sequences that multiply by the same number each time: the $n$ th term, the sum of the first $n$ terms and its proof, finding unknowns, and the growth and decay problems they model.
≈ 45 min
Sum to infinity
How adding infinitely many numbers can give a finite answer, the condition $|r|<1$ that makes it happen, and how to use $S_\infty=\dfrac{a}{1-r}$ for recurring decimals, bouncing balls and exam problems.
≈ 35 min
Binomial expansion for any rational n
Extending $(1+x)^n$ to negative and fractional powers: an infinite series that only works for $|x|<1$ , how to handle $(a+bx)^n$ , and how to use the expansion with partial fractions and for approximations.
≈ 45 min