3.3.1 Sequences and series (A-level only)

A sequence of daily depth changes in a reservoir, $x1,x2,x3,…x_1, x_2, x_3, \dots$ , is defined by the recurrence relation

x_{n+1} = 2(x_n + 2)^2 - 10

x_1 = k - 2

where $k$ is a constant.

a.

Find an expression for $x_2$ in terms of $k$ , giving your answer in simplest form.

[2]

b.

Given that $∑n=13xn=k+22\sum_{n=1}^{3} x_n = k + 22$

find the possible values of $x_2$ .

[5]

A sequence of daily depth changes in a reservoir, $x1,x2,x3,…x_1, x_2, x_3, \dots$ , is defined by the recurrence relation

x_{n+1} = 2(x_n + 2)^2 - 10

x_1 = k - 2

where $k$ is a constant.

a.

Find an expression for $x_2$ in terms of $k$ , giving your answer in simplest form.

[2]

b.

Given that $∑n=13xn=k+22\sum_{n=1}^{3} x_n = k + 22$

find the possible values of $x_2$ .

[5]

3.3.1 Sequences and series (A-level only) Questions