1. **Stating the problem:** We have a sequence of figures where each figure is a large triangle subdivided into smaller triangles. The first figure has 1 small triangle, the second has 4 small triangles, and the third has 16 small triangles. We want to find the number of small triangles in the 10th figure. 2. **Observing the pattern:** The number of small triangles in each figure seems to be powers of 4: - 1st figure: $1 = 4^0$ - 2nd figure: $4 = 4^1$ - 3rd figure: $16 = 4^2$ 3. **General formula:** The number of small triangles in the $n$th figure is given by: $$\text{Number of small triangles} = 4^{n-1}$$ 4. **Applying the formula for the 10th figure:** $$4^{10-1} = 4^9$$ 5. **Calculating $4^9$:** $$4^9 = (2^2)^9 = 2^{18} = 262144$$ 6. **Answer:** The 10th figure contains $262144$ small triangles. This means the large triangle in the 10th term is subdivided into 262144 smaller triangles arranged in a 10-level triangular grid.