Find the first three terms of the expansion of (9+2x)−12\displaystyle (9 + 2x)^{-\frac{1}{2}}(9+2x)−21 in ascending powers of xxx, giving each coefficient in its simplest form.
The expansion of
a+bx9+2x\displaystyle \frac{a + bx}{\sqrt{9 + 2x}}9+2xa+bx
in ascending powers of x x\,x begins 3+x+…3 + x + \dots3+x+…
Find the value of a a\,a and the value of bbb.
308 exam-style questions on AQA A Level Maths 1.7 D: Sequences and series, covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.