March 2009

### Step 1 — Solution

The first row starts with the number 4. The starting number of any other row is 3 steps on from that of the previous one. This tells us that the first number in row *m* is of the form

*m*+ 1.

The difference between successive numbers in the first row is 3, and the difference between successive numbers in any other row is 2 greater than the difference in the previous row. This means that the difference between successive numbers in row *m* is

*m*+ 1.

The *n*th entry in row *m* is equal to the first entry plus (*n*-1) times the difference in that row, so the *n*th entry in row *m* is

*m*+ 1 + (n-1) (2

*m*+ 1) = (2

*n*+1)

*m*+

*n*.