Matchstick Patterns

Transcript

Matchstick PatternsLet’s look at this pattern and identify the expression We observe that To make 1 triangle uses 3 matchsticks. To make 2 triangles use 5 matchsticks. To make 3 triangles use 7 matchsticks. The general rule is that you start with 3 matchsticks for the first triangle, and then add 2 more matchsticks for each new triangle you add to the chain The formula is: Number of matchsticks = 2t + 1, where ‘t' is the number of triangles We can think of this like his method follows the logic of starting with the first triangle and adding two sticks for each subsequent one. You start with 3 matchsticks for the first step. For two triangles, there are 2 more match sticks For three triangles, we add 2 more matchsticks So, every step, we add two matchsticks For three triangles, we added total 4 (2 × 2) matchsticks from initial 3 For four triangles, we added total 6 (3 × 2) matchsticks from initial 3 So, for ‘t’ triangles, we will add (t – 1) × 2 matchsticks Thus, our formula becomes 3 + (t – 1) × 2 Simplifying expression 3 + (t – 1) × 2 = 3 + 2t – 2 = 1 + 2t = 2t + 1 We can also observe the same from this table