a)Pattern number 6 has 26 sticks.
b) Pattern number n has 4n - 2 sticks.
a) Pattern number 6:
1. Each pattern starts with 2 sticks.
2. For each subsequent pattern, you add 4 sticks to the previous pattern.
3. Therefore, for pattern 6, you have: 2 sticks (initial) + 4 sticks (pattern 1) + 4 sticks (pattern 2) + 4 sticks (pattern 3) + 4 sticks (pattern 4) + 4 sticks (pattern 5) = 26 sticks.
b) Pattern number n:
1. Following the same logic, the number of sticks in pattern n can be expressed as a formula:
2. Number of sticks = 2 sticks (initial) + 4 sticks/pattern * (n patterns - 1)
3. Simplifying the equation: Number of sticks = 2 + 4(n - 1)
4. Combining like terms: Number of sticks = 4n - 2
Therefore:
- a) Pattern number 6 has 26 sticks.
- b) Pattern number n has 4n - 2 sticks.