Answer
f(n) = 3ⁿ⁻¹ = 3^(n - 1)
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!!!
