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.
Find an expression for x2 x_2\,x2 in terms of kkk.
Show that x3=16k−5x_3 = 16k - 5x3=16k−5.
Find ∑r=14ar\sum_{r=1}^4 a_r∑r=14ar in terms of kkk.
178 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.