1

The population of a town is modelled by $P_{n+1} = a\,P_n + 800$, where $P_n$ is the population at the start of year $n$.
At the start of year 1 the population is $30000$, and at the start of year 2 it is $36800$.
Use the model to work out the population at the start of year 4. [3]

2

Here is a sequence with one term missing.
$44,\ \boxed{\phantom{00}},\ 38,\ 35,\ 32$
Work out the value of the missing term. [2]

3

The $n$th term of a sequence is $n^2 + 1$.
Work out the smallest integer $n$ for which the $n$th term is greater than $600$. [2]

4

Each term of this Fibonacci-type sequence is the sum of the two terms before it.
$5,\ 2,\ 7,\ \boxed{\phantom{0}},\ 16$
Work out the missing term. [2]