A sequence a1,a2,a3,… a_1, a_2, a_3, \dots\,a1,a2,a3,… is defined by an+1=k−anan\displaystyle a_{n+1} = \frac{k - a_n}{a_n}an+1=ank−an where k k\,k is a constant. k2−11k−12=0k^2 - 11k - 12 = 0k2−11k−12=0, k≠12 k \neq 12\,k=12 and a1=3a_1 = 3a1=3.
Find the value of kkk.
Show that the sequence is periodic of order 3.
Find the value of ∑r=1100ar\sum_{r=1}^{100} a_r∑r=1100ar.
326 exam-style questions on Edexcel A Level Maths Sequences and Series, covering 3.1 Arithmetic Sequences, 3.2 Arithmetic Series, 3.3 Geometric Sequences, 3.4 Geometric Series, 3.5 Sum to Infinity, 3.6 Sigma Notation, 3.7 Recurrence Relations, and 3.8 Modelling with Series. Each one has a worked solution and a mark scheme showing where the marks go.