a) By observing the pattern carefully,itcanbeconcludedthatthenumberofmatchsticks is `4, 7, 10, `and `13 `which is 1 morethanthricethe numberofsquarespresent i.e, 1 square =` 3 xx 1 + 1 = 4 `matchsticks, 2 squares =` 3 xx 2 + 1=7` matchsticks and so on.. Thus, the rule for this pattern = 3n + 1 where,n=numberofsquares b) Similarly, by observing the above matchstick pattern of triangles, we can conclude that every consecutive triangle shares a common matchstick. Thenumberofmatchsticks in the first pattern is 3, i.e,` 2 xx 1 + 1 = 3`
The number of matchsticks in the second pattern is 5, i.e,` 2 xx 2 + 1 = 5`
The number of matchsticks in the third pattern is 7, i.e,` 2 xx3 + 1 = 7`
Thus, the pattern generated is adding 1 matchstick to twice the number of triangles present
Hence, the general rule for the pattern of triangles is `2n + 1` where, n = number of triangles