To solve the problem for the given function [tex]\( f(n) = 7n - 13 \)[/tex], let's break it down step by step:
### Step 1: Identify the Function and its Form
The given function is:
[tex]\[ f(n) = 7n - 13 \][/tex]
This is a linear function where:
- The coefficient of [tex]\( n \)[/tex] is the common difference in an arithmetic sequence.
- The constant term indicates the value when [tex]\( n = 0 \)[/tex], which helps to determine the starting value of the sequence.
### Step 2: Determine the Common Difference
In any linear function of the form [tex]\( f(n) = an + b \)[/tex], the coefficient [tex]\( a \)[/tex] represents the common difference in an arithmetic sequence. Here, the coefficient of [tex]\( n \)[/tex] is 7. Therefore, the common difference is:
[tex]\[ \text{Common Difference} = 7 \][/tex]
### Step 3: Calculate the Starting Value
The starting value of the sequence can be found by evaluating the function at [tex]\( n = 0 \)[/tex]:
[tex]\[ f(0) = 7 \cdot 0 - 13 = -13 \][/tex]
Thus, the starting value is:
[tex]\[ \text{Starting Value} = -13 \][/tex]
### Summary
From the steps above, we have determined that for the given function [tex]\( f(n) = 7n - 13 \)[/tex]:
- The common difference is 7.
- The starting value is -13.
So, the answer is:
[tex]\[ \text{Common Difference: } 7 \quad \text{Starting Value: } -13 \][/tex]
