1. **Problem:** How many triangular tiles are there in the FIFTH figure of the sequence? 2. **Understanding the pattern:** The sequence shows triangular tiles increasing in a pattern. Let's analyze the number of tiles in each figure. 3. **Observing the pattern:** - Figure 1: 1 black tile + 0 gray tiles = 1 tile - Figure 2: 1 black tile + 3 gray tiles = 4 tiles - Figure 3: 1 black tile + 6 gray tiles = 7 tiles - Figure 4: 1 black tile + 10 gray tiles = 11 tiles 4. **Identifying the pattern in gray tiles:** The gray tiles follow triangular numbers: 0, 3, 6, 10, ... which correspond to $T_n = \frac{n(n+1)}{2}$ for $n=0,2,3,4,...$ but here it seems to be the sum of the first $n$ natural numbers minus 1. 5. **Calculating the number of tiles in the 5th figure:** The gray tiles for figure 5 are $T_5 = \frac{5 \times 6}{2} = 15$. Total tiles = 1 black + 15 gray = 16 tiles. 6. **Answer:** The number of triangular tiles in the fifth figure is **16**. **Final answer:** c. 16