38 13. A sequence of numbers a1, a2, a3, … is defined by an+1 = k a a n n + ( ) 2 n   where k is a constant. Given that ● the sequence is a periodic sequence of order 3 ● a1 = 2 (a) show that k2 + k − 2 = 0 (3) (b) For this sequence explain why k ≠ 1 (1) (c) Find the value of ar r=∑ 1 80 (3) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________