Here is the solution and explanation for each question in the image:

Problem 1:

Inputs and Outputs:

The output is calculated using the formula $6(n) + 1$, where $n$ is the input.

• For $n = 1$: $6(1) + 1 = 7$
• For $n = 2$: $6(2) + 1 = 13$
• For $n = 3$: $6(3) + 1 = 19$
• For $n = 4$: $6(4) + 1 = 25$
• For $n = 5$: $6(5) + 1 = 31$

Rule as an Expression: $6n + 1$

Problem 2:

Inputs and Outputs:

The relationship between input and output appears to follow the rule $10(n - 1) - 1$. Simplifying this: $10n - 1.$

• For $n = 1$: $10(1) - 1 = 9$
• For $n = 2$: $10(2) - 1 = 19$
• For $n = 3$: $10(3) - 1 = 29$
• For $n = 4$: $10(4) - 1 = 39$

Rule as an Expression: $10n - 1$

Problem 3:

Inputs and Outputs:

This problem involves multiplication. The output is $25 \times n$, where $n$ is the input.

• For $n = 1$: $25 \times 1 = 25$
• For $n = 2$: $25 \times 2 = 50$
• For $n = 3$: $25 \times 3 = 75$
• For $n = 4$: $25 \times 4 = 100$
• For $n = 5$: $25 \times 5 = 125$

Rule as an Expression: $25n$

Rule in Words: Multiply the input by 25.

Problem 4:

Inputs and Outputs:

The output is calculated by doubling the input. The rule is $2 \times n$, or $2n$, where $n$ is the input.

• For $n = 1$: $2 \times 1 = 8$
• For $n = 2$: $2 \times 2 = 10$
• For $n = 3$: $2 \times 3 = 12$
• For $n = 4$: $2 \times 4 = 14$
• For $n = 5$: $2 \times 5 = 16$

Rule as an Expression: $2n + 6$