1.4.5 Sequences (A-level only)

A robotic arm moves along a linear track. Its position $p_n$ (in cm) at step $n\,$ is governed by the recurrence relation:

p_{n+1} = 3 - (p_n)^2

a.

In the case where the arm starts at $p_1 = 2$ :

(i) Find the value of $p_3$ .

(ii) Determine the value of $p_{100}$ .

[4]

b.

State a different value for $p_1$ , other than $p_1 = 2$ , which gives the same value for $p_{100}$ as found in part (a)(ii).

[2]

A robotic arm moves along a linear track. Its position $p_n$ (in cm) at step $n\,$ is governed by the recurrence relation:

p_{n+1} = 3 - (p_n)^2

a.

In the case where the arm starts at $p_1 = 2$ :

(i) Find the value of $p_3$ .

(ii) Determine the value of $p_{100}$ .

[4]

b.

State a different value for $p_1$ , other than $p_1 = 2$ , which gives the same value for $p_{100}$ as found in part (a)(ii).

[2]

1.4.5 Sequences (A-level only) Questions