A sequence x1,x2,x3,… x_1, x_2, x_3, \dots\,x1,x2,x3,… is defined by x1=kx_1 = kx1=k and xn=4xn−1−1,n≥2x_n = 4x_{n-1} - 1, \quad n \geq 2xn=4xn−1−1,n≥2.
Verify that x2=4k−1x_2 = 4k - 1x2=4k−1.
Show that x3=16k−5x_3 = 16k - 5x3=16k−5.
Find ∑r=14xr\sum_{r=1}^4 x_r∑r=14xr in terms of kkk.
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.