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1. Consider the following sequence of triangles.Write an equation to find the number oftriangles f(n) in the nth group.

1. Consider the following sequence of triangles.Write an equation to find the number-example-1
User Treps
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1 Answer

1 vote

Answer

f(n) = 3ⁿ⁻¹ = 3^(n - 1)

Step-by-step explanation

We can see that the first figure has only 1 black triangle.

The second figure has 3 black triangles.

The third figure has 9 black triangles.

We can see a pattern here that the number of black triangles keep increasing in a noticeable pattern.

1, 3, 9, ......

1 = 3⁰

3 = 3¹

9 = 3²

If the first term is n = 1, we can see that the pattern for f(n) is 3ⁿ⁻¹

f(n) = 3ⁿ⁻¹

f(n = 1) = 3¹⁻¹ = 3⁰ = 1

f(n = 2) = 3²⁻¹ = 3¹ = 3

f(n = 3) = 3³⁻¹ = 3² = 9

Hope this Helps!!!

User Xno
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