A sequence a1,a2,a3,… a_1, a_2, a_3, \dots\,a1,a2,a3,… is defined by
an+1=k−anana_{n+1} = \dfrac{k - a_n}{a_n}an+1=ank−an
where k k\,k is a constant. The sequence is periodic of order 3 and a1=3a_1 = 3a1=3.
Show that k2−11k−12=0k^2 - 11k - 12 = 0k2−11k−12=0.
For this sequence, explain why k≠12k \neq 12k=12.
Find the value of ∑r=1100ar\sum_{r=1}^{100} a_r∑r=1100ar.
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.