A builder is making fences using square blocks. Each 'Term' shows a new section of the fence. Your challenge is to figure out the **perimeter** of the fence sections!
Unpacking the Fence Perimeters!
Let's look at how the perimeter changes with each added block:
- Term 1 (1 block): A single square. Perimeter = 4 sides = 4 units.
- Term 2 (2 blocks): Two squares side-by-side. The shared side disappears from the perimeter.
Original: 4 + 4 = 8. Shared: 2 sides. So, 8 - 2 = 6 units.
- Term 3 (3 blocks): Three squares in a row.
Original: 4 + 4 + 4 = 12. Shared: 4 sides (2 pairs). So, 12 - 4 = 8 units.
The pattern is that the perimeter increases by 2 units for each new term.
Solving the Questions:
1. What is the perimeter of Term 4?
- Term 3 was 8 units. Add 2 for Term 4: 8 + 2 = 10 units.
2. What is the perimeter of Term 10?
- The perimeter starts at 4 (for n=1) and increases by 2 for each subsequent term.
This is a linear pattern: P = 2n + C.
For n=1, P=4: 4 = 2(1) + C → C = 2.
So, the formula is P = 2n + 2.
- For Term 10: 2 * 10 + 2 = 20 + 2 = 22 units.
3. If 'n' represents the term number, which formula correctly describes the perimeter of Term 'n'?
- As derived above, the formula is 2n + 2.
- For n=1: 2(1) + 2 = 4
- For n=2: 2(2) + 2 = 6
- For n=3: 2(3) + 2 = 8