1

A growing pattern uses square tiles.
Pattern 1 uses $6$ square tiles, Pattern 2 uses $8$ and Pattern 3 uses $10$.
How many more square tiles are needed to go from one pattern to the next?

2

The $n$th term of a sequence is $n^2 + 5$.
Work out the smallest integer $n$ for which the $n$th term is greater than $250$.

3

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 $25000$, and at the start of year 2 it is $30800$.
Use the model to work out the population at the start of year 4.