Question

Sonam says that the 20th figure in this pattern has 400 small triangles. do you agree? explain your thinking. ​

Answer 1

No. There should be 210 small triangles

Explanation:

The number of small triangles in these figures forms a sequence

Fig No Small Triangles
1 1
2 3 (1+2)
3 6 (1+2+3)

So the nth figure should have 1+2+3+.....+(n-1)+ n

1+2+3+.....+(n-1)+ n =
`(n (n-1))/(2)`
So for 20th figure, n = 20 and number of small triangles = 20 x 21 /2 = 420/2 = 210