C1 January 2006 Q2

EdexcelOld spec4 marksSequences & Series

2. The sequence of positive numbers \(u_1, u_2, u_3, \ldots\) is given by:\[u_{n+1} = (u_n - 3)^2, \qquad u_1 = 1.\]

(a) Find \(u_2\), \(u_3\) and \(u_4\). (3)

(b) Write down the value of \(u_{20}\). (1)

Mark scheme (a)

Scheme	Marks
\(u_2 = (-2)^2 = 4\)	B1
\(u_3 = 1,\ u_4 = 4\) For \(u_3\), ft \((u_2 - 3)^2\)	B1ft, B1
	(3)

Notes

Do not give marks if answers have clearly been obtained from wrong working,
e.g. \(u_2 = (3 - 3)^2 = 0\)
\(u_3 = (4 - 3)^2 = 1\)
\(u_4 = (5 - 3)^2 = 4\)

Scheme	Marks
\(u_{20} = 4\)	B1ft
	(1)
	(4 marks)