Edexcel A-Level Mathematics AS P2.4.1 Sequences Questions

Practise Edexcel IAL Mathematics P2.4.1 by iterating recurrence rules, applying given term or sum conditions and substituting terms into finite series.

Exam points

generate successive terms such as u2, u3 or u5 from the recurrence relation
use a given sequence condition such as a term or finite sum to form and solve an equation for k
substitute generated terms into a finite sum such as Σu_r to determine the constant

[Maximum number: 5]

A sequence is defined by

\begin{aligned} u_{1} & =6 \\ u_{n+1} & =k u_{n}+3 \end{aligned}

where k is a positive constant.

(a)

Find, in terms of k, an expression for $u_{3}$

Given that $\sum_{n=1}^{3} u_{n}=117$

[ 2 ]

Substitute $u_2=6k+3$ into $u_3=ku_2+3$ :
$u_3=k(6k+3)+3=6k^2+3k+3.$

(b)

find the value of k.

[ 3 ]

M1: Sets their $u_{1}+u_{2}+u_{3}=117$ to produce an equation in just k.
dM1: Solves a 3TQ by any valid method to find at least one value for k.
A1: $\quad k=\frac{7}{2}$ ONLY

Figure for Answer to Question (b) — Edexcel A-Level Mathematics AS

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Edexcel A-Level Mathematics AS P2.4.1 Sequences Questions question 1

Question (a)

Question (b)