Question

(a) Look at the following matchstick pattern of squares. The squares are not separate. Two neighbouring squares have a common matchstick. Observe the patterns and find the rule that gives the number of matchsticks in terms of the number of squares. (Hint: if you remove the vertical stick at the end, you will get a pattern of Cs.)

(b) The given figure gives a matchstick pattern of triangles. Find the general rule that gives the number of matchsticks in terms of the number of triangles.

Answer 1

(a) It can be observed that in the given matchstick pattern, the number of

matchsticks are 4, 7, 10, and 13, which is 1 more than thrice of the number of squares in the pattern.

Hence, the pattern is 3n + 1, where n is the number of squares.

(b) It can be observed that in the given matchstick pattern, the number of

matchsticks are 3, 5, 7, and 9, which is 1 more than twice of the number of triangles in the pattern.

Hence, the pattern is 2n + 1, where n is the number of triangles.