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

Sonam Says That The 20th Figure In This Pattern Has 400 Small Triangles Do You Agree Explain Your Thinking class=

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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

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