Question

Look at the following matchstick pattern of squares. The squares are not separate. Two neighboring squares have a common matchstick. Observe the patterns and find the rule that gives the number of matchsticks.

Answer 1

Here, in each step one square is being added. So the repetitive pattern is ‘square’.

For making one square, 4 matchsticks are used.

At level 2, one more square is added. So, the number of matchsticks used for making two squares is 7.

At level 3, one more square is added. So, the number of matchsticks used for making three squares is 10.

By observing the pattern carefully, it can be concluded that the number of matchsticks is 4, 7, 10, and 13 which is 1 more than thrice the number of squares present

For 1 square, number of matchsticks used
⇒ 3 × 1 + 1 = 4

Similarly, for 2 squares, the number of matchsticks used:
⇒ 3 × 2 + 1 = 7 and so on.

Thus, the rule for this pattern will be 3n + 1 where n is the number of squares present at each level.