If n, p, q, and r are consecutive integers, what is their sum?

Answer

To find the sum of four consecutive integers \( n, p, q, \) and \( r \), we can express these integers in terms of \( n \):

1. Let \( n \) be the first integer.
2. The next consecutive integers can be expressed as:
- \( p = n + 1 \)
- \( q = n + 2 \)
- \( r = n + 3 \)

Now, we can write the sum of these four integers:

\[ \text{Sum} = n + p + q + r \]

Substituting the expressions for \( p, q, \) and \( r \):

\[ \text{Sum} = n + (n + 1) + (n + 2) + (n + 3) \]

Now, combine like terms:

\[ \text{Sum} = n + n + 1 + n + 2 + n + 3 \]
\[ \text{Sum} = 4n + (1 + 2 + 3) \]
\[ \text{Sum} = 4n + 6 \]

Thus, the sum of the four consecutive integers \( n, p, q, \) and \( r \) is:

\[ \text{Sum} = 4n + 6 \]

Next, we can analyze whether this sum is even or odd. Since \( 4n \) is always even (as it is a multiple of 4), and 6 is also even, the sum of two even numbers is always even. Therefore, the sum \( 4n + 6 \) is even.

### Final Answer:
The sum of the four consecutive integers \( n, p, q, \) and \( r \) is \( 4n + 6 \), which is even.