1.4.5 Sequences (A-level only)

A sequence of sensor measurements $P1,P2,P3,…P_1, P_2, P_3, \dots$ is defined by the recurrence relation

P_{n+1} = 2(P_n - 3)^2 - 4, \quad n \ge 1

where the first measurement is given by $P_1 = k + 3$ and $k$ is a constant.

a.

Find an expression for $P_2$ in terms of $k$ , giving your answer in its simplest form.

[2]

b.

Given that $∑n=13Pn=k+12\sum_{n=1}^{3} P_n = k + 12$ ,

determine the possible values of $P_2$ .

[6]

A sequence of sensor measurements $P1,P2,P3,…P_1, P_2, P_3, \dots$ is defined by the recurrence relation

P_{n+1} = 2(P_n - 3)^2 - 4, \quad n \ge 1

where the first measurement is given by $P_1 = k + 3$ and $k$ is a constant.

a.

Find an expression for $P_2$ in terms of $k$ , giving your answer in its simplest form.

[2]

b.

Given that $∑n=13Pn=k+12\sum_{n=1}^{3} P_n = k + 12$ ,

determine the possible values of $P_2$ .

[6]

1.4.5 Sequences (A-level only) Questions