1. The problem asks to find the next two terms in the sequence of triangular numbers: 1, 3, 6, 10, 15, ... 2. Triangular numbers are given by the formula $$T_n = \frac{n(n+1)}{2}$$ where $n$ is a positive integer representing the term position. 3. The given terms correspond to $n=1$ to $n=5$: - $T_1 = \frac{1 \times 2}{2} = 1$ - $T_2 = \frac{2 \times 3}{2} = 3$ - $T_3 = \frac{3 \times 4}{2} = 6$ - $T_4 = \frac{4 \times 5}{2} = 10$ - $T_5 = \frac{5 \times 6}{2} = 15$ 4. To find the next two terms, calculate $T_6$ and $T_7$: $$T_6 = \frac{6 \times 7}{2} = \frac{42}{2} = 21$$ $$T_7 = \frac{7 \times 8}{2} = \frac{56}{2} = 28$$ 5. Therefore, the next two terms in the sequence are 21 and 28. 6. In summary, the sequence continues as: 1, 3, 6, 10, 15, 21, 28.