1. **Problem Statement:** We have a triangular pattern of solar cells where the number of cells added at each stage increases by 1, starting from 1 cell at stage 1. 2. **Formula and Explanation:** The total number of cells at stage $n$ is the $n$th triangular number given by: $$T_n = \frac{n(n+1)}{2}$$ This formula sums the first $n$ natural numbers. 3. **Step-by-step for Question 26:** - Stage 1: $T_1 = \frac{1 \times 2}{2} = 1$ - Stage 2: $T_2 = \frac{2 \times 3}{2} = 3$ - Stage 3: $T_3 = \frac{3 \times 4}{2} = 6$ - Stage 4: $T_4 = \frac{4 \times 5}{2} = 10$ - Stage 5: $T_5 = \frac{5 \times 6}{2} = 15$ **Answer:** 15 cells (Option C). 4. **Step-by-step for Question 27:** Calculate total cells up to stage 8: $$T_8 = \frac{8 \times 9}{2} = 36$$ **Answer:** 36 cells (Option D). 5. **Step-by-step for Question 28:** Calculate max racks based on each component: - Panels long: $\lfloor \frac{26}{4} \rfloor = 6$ - Panels short: $\lfloor \frac{33}{6} \rfloor = 5$ - Clips small: $\lfloor \frac{200}{12} \rfloor = 16$ - Clips large: $\lfloor \frac{20}{2} \rfloor = 10$ - Screws: $\lfloor \frac{510}{14} \rfloor = 36$ The limiting factor is panels short = 5 racks. **Answer:** 5 racks (Option B). 6. **Step-by-step for Question 29:** Check each statement for 6 racks: - Panels short needed: $6 \times 6 = 36$, stock 33, need 3 more (statement 1 true). - Panels long needed: $6 \times 4 = 24$, stock 26, leftover 2 (statement 2 true). - Clips large needed: $6 \times 2 = 12$, stock 20, leftover 8, so no need additional 8 (statement 3 false). - Screws leftover: $510 - 6 \times 14 = 510 - 84 = 426$ (statement 4 false). **Answer:** Statements (1) and (2) are true (Option A).