Sonam says that the 20th figure in this pattern has 400 small triangles. do you agree? explain your thinking.
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Answer:
No. There should be 210 small triangles
Step-by-step 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 = [tex]\frac{n (n-1)}{2}[/tex]
So for 20th figure, n = 20 and number of small triangles = 20 x 21 /2 = 420/2 = 210