Pattern True False 9A35F3

1. **Problem:** Determine the truth values for the statements about the pattern starting with $5$ and multiplying by $3$ each time. 2. **Step 1: Understand the pattern** - The first term is $5$. - Each subsequent term is obtained by multiplying the previous term by $3$. - So the terms are: $5, 5 \times 3 = 15, 15 \times 3 = 45, 45 \times 3 = 135, \ldots$ 3. **Check each statement:** - "All terms are multiples of $5$": Since the first term is $5$ and each term is multiplied by $3$, every term is $5 \times 3^n$ for some $n \geq 0$, so all terms are multiples of $5$. **True**. - "All terms are multiples of $3$": The first term $5$ is not a multiple of $3$, so this is **False**. - "All terms are even numbers": The first term $5$ is odd, so this is **False**. 4. **Summary for question 1:** - All terms are multiples of $5$: True - All terms are multiples of $3$: False - All terms are even numbers: False --- 5. **Problem 2:** Analyze the statements about the rows of circles. 6. **Step 1: Understand the statements:** - "Each row grows by $1$": This means the number of circles in each row increases by $1$ compared to the previous row. - "The circles always add up to an odd number": The total number of circles in each row is always odd. - "The rows alternate from odd to even": The number of circles in rows alternates between odd and even counts. 7. **Step 2: Analyze each statement:** - If each row grows by $1$, starting from some number, the counts increase by $1$ each time. - If the first row has an odd number of circles, the next row will have an even number, then odd, then even, alternating. - Therefore, "Each row grows by $1$" is likely **True**. - "The circles always add up to an odd number" is **False** because the number alternates. - "The rows alternate from odd to even" is **True**. 8. **Summary for question 2:** - Each row grows by $1$: True - The circles always add up to an odd number: False - The rows alternate from odd to even: True **Final answers:** 1. - All terms are multiples of $5$: True - All terms are multiples of $3$: False - All terms are even numbers: False 2. - Each row grows by $1$: True - The circles always add up to an odd number: False - The rows alternate from odd to even: True