The given figure gives a match stick pattern of triangles. Find the general rule that gives the number of matchsticks in terms of the number of triangles.

 

Solution

From the figure we observe that in the given matchstick pattern, the number of matchsticks are 3, 5, 7 and 9 which is 1 more than the twice of the number of triangles in the pattern.

The number of matchsticks used in each pattern is 1 more than 2 times the number of triangles in it.

Therefore the pattern is 2x + 1, where x is the number of triangles.