A sequence u1,u2,u3,… u_1, u_2, u_3, \dots\,u1,u2,u3,… is defined by
u1=1u_1 = 1u1=1
un+1=(un−1)2u_{n+1} = (u_n - 1)^2un+1=(un−1)2, n≥1n \geq 1n≥1
Find u2u_2u2, u3 u_3\,u3 and u4u_4u4.
Write down the value of u100u_{100}u100.
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.