1. **State the problem:** We want to find how many counters (dots) are in the 10th term of the given pattern. 2. **Analyze the pattern:** - The 1st term has 1 row with 3 dots. - The 2nd term has 2 rows: 5 dots in the 1st row, 2 dots in the 2nd row. - The 3rd term has 3 rows: 7, 5, and 3 dots respectively. - The 4th term has 4 rows: 9, 7, 5, and 3 dots. 3. **Identify the pattern in each row:** - The bottom row always has 3 dots. - Each row above increases by 2 dots compared to the row below. 4. **Generalize the number of dots in each row for the nth term:** - The nth term has n rows. - The bottom row has 3 dots. - The row above has 3 + 2 = 5 dots. - The next row above has 3 + 4 = 7 dots, and so on. So, the number of dots in the $k^{th}$ row from the bottom is: $$\text{dots}_k = 3 + 2(k-1)$$ where $k=1$ is the bottom row, $k=n$ is the top row. 5. **Calculate the total dots in the 10th term:** Sum the dots in all 10 rows: $$\text{Total} = \sum_{k=1}^{10} [3 + 2(k-1)] = \sum_{k=1}^{10} (3 + 2k - 2) = \sum_{k=1}^{10} (1 + 2k)$$ 6. **Simplify the sum:** $$\text{Total} = \sum_{k=1}^{10} 1 + \sum_{k=1}^{10} 2k = 10 + 2 \sum_{k=1}^{10} k$$ 7. **Calculate the sum of the first 10 natural numbers:** $$\sum_{k=1}^{10} k = \frac{10 \times 11}{2} = 55$$ 8. **Calculate the total:** $$\text{Total} = 10 + 2 \times 55 = 10 + 110 = 120$$ **Final answer:** The 10th term has 120 counters. None of the options A (23), B (35), C (40), or D (80) match 120, so the correct total is 120 counters.