Question

A computer engineer wrote a software program that assigns a value each time the program is run. The first 5 assigned values are listed below.

–2, 5, 12, 19, 26

Which formula did the engineer use to determine the assigned values, where n is the number of times the program was run?

A.

B.

C.

D.

Answer 1

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:

\[
\boxed{7n - 9}
\]