To find the formula that generates the assigned values based on the sequence given, we can analyze the pattern of the values provided: -2, 5, 12, 19, 26.
First, let’s denote the assigned values by \( V(n) \), where \( n \) is the number of times the program was run. We can look at the sequence of values for different values of \( n \):
- \( V(1) = -2 \)
- \( V(2) = 5 \)
- \( V(3) = 12 \)
- \( V(4) = 19 \)
- \( V(5) = 26 \)
Next, we can calculate the difference between each successive value in the sequence:
\[ \begin{align*} 5 - (-2) &= 7 \ 12 - 5 &= 7 \ 19 - 12 &= 7 \ 26 - 19 &= 7 \ \end{align*} \]
The common difference is 7, which indicates that this is an arithmetic sequence with a constant difference of 7.
The formula for the \( n \)-th term of an arithmetic sequence can be expressed as:
\[ V(n) = V(1) + (n - 1) \cdot d \]
where \( V(1) \) is the first term, \( d \) is the common difference, and \( n \) is the term number.
Substituting the values we know:
- The first term \( V(1) = -2 \)
- The common difference \( d = 7 \)
We can write:
\[ V(n) = -2 + (n - 1) \cdot 7 \]
Simplifying this expression gives:
\[ V(n) = -2 + 7n - 7 = 7n - 9 \]
Thus, the formula that the engineer used to determine the assigned values is:
\[ \boxed{7n - 9} \]
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