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 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.