A sequence x1,x2,x3,… x_1, x_2, x_3, \dots\,x1,x2,x3,… is defined by
x1=kxn=4xn−1−1,n≥2 \begin{aligned}x_1 &= k \\x_n &= 4x_{n-1} - 1, \quad n \geq 2\end{aligned} x1xn=k=4xn−1−1,n≥2Find an expression for x2 x_2\,x2 in terms of kkk.
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.
6 exam-style questions on AQA A Level Maths 1.7.3 Sigma notation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.