With 3 toothpicks you can make a triangle. To form a row with 2 triangles, 5 toothpicks are needed. A row of 3 triangles uses 7 matchsticks, but if it contains 5 triangles, 11 matchsticks are used, and so on. Matchstick triangles To form a row of n triangles, the number of matchsticks needed can be calculated with the expression.

Let's denote the number of matchsticks needed to form a row of n triangles as M(n).

We can observe that each additional triangle in the row requires 2 additional matchsticks compared to the previous row. So, we can write the relationship as:

M(n) = M(n-1) + 2

where M(n-1) represents the number of matchsticks needed to form a row of (n-1) triangles.

To find the expression for M(n) in terms of n, we can use the initial values provided in the problem:

M(1) = 3 (as we need 3 matchsticks to form a single triangle)
M(2) = 5 (as we need 5 matchsticks to form a row of 2 triangles)

Using these initial values, we can create a table to find the expression for M(n):

| n | M(n) |
|---|-------|
| 1 | 3 |
| 2 | 5 |
| 3 | 7 |
| 4 | 9 |
| 5 | 11 |
|...| ... |

From the table, we can observe that M(n) can be calculated using the expression:

M(n) = 2n + 1

Answer: $$M(n) = 2n + 1$$