Edexcel IAL Mathematics P2.4.1 sequences

The direct evidence focuses on recurrence work: calculate u2, u3 or u5 from the rule, substitute a given condition and solve the resulting equation for k.

Exam points

Generate successive terms such as u2, u3 or u5 from the recurrence relation.
Use a given term condition like u3 = 6 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 $u_3=ku_2+3$ :
$u_3=k(6k+3)+3=6k^2+3k+3.$
M1 A1

(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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P2.4.1 - Sequences, question 1

Question (a)

Question (b)