A sequence a1,a2,a3,… a_1, a_2, a_3, \dots\,a1,a2,a3,… is defined by
a1=1,a2=6an=an−1+an−2,n≥3 \begin{aligned}a_1 &= 1, a_2 = 6 \\a_n &= a_{n-1} + a_{n-2}, \quad n \geq 3\end{aligned} a1an=1,a2=6=an−1+an−2,n≥3Find a3,a4 a_3, a_4\,a3,a4 and a5a_5a5.
308 exam-style questions on OCR A Level Maths 1.4 Sequences and Series, covering 1.4.1 Binomial expansion for positive integer n, 1.4.2 Link to binomial probabilities, 1.4.3 Binomial expansion for rational n (A-level only), 1.4.4 Validity of the expansion (A-level only), 1.4.5 Sequences (A-level only), 1.4.6 Increasing, decreasing and periodic sequences (A-level only), 1.4.7 Sigma notation (A-level only), 1.4.8 Arithmetic sequences and series (A-level only), 1.4.9 Geometric sequences and series (A-level only), 1.4.10 Sum to infinity of a geometric series (A-level only), and 1.4.11 Modelling with sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.