How many terms are there in the set of consecutive integers from `-18` to 33, inclusive?

Answer

To find the number of terms in the set of consecutive integers from -18 to 33, inclusive, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the first and last terms**:
- The first term (A) is -18.
- The last term (L) is 33.

2. **Understand the concept of consecutive integers**:
- Consecutive integers are integers that follow one after the other without any gaps. In this case, we are looking at integers from -18 to 33.

3. **Use the formula for the number of terms in an arithmetic progression (AP)**:
- The formula to find the number of terms (N) in an AP is given by:
\[ N = \frac{L - A}{D} + 1 \]
- Where:
- \(L\) = last term
- \(A\) = first term
- \(D\) = common difference (for consecutive integers, \(D = 1\))

4. **Substitute the values into the formula**:
- Here, \(L = 33\), \(A = -18\), and \(D = 1\).
- Plugging in the values:
\[ N = \frac{33 - (-18)}{1} + 1 \]

5. **Calculate the difference**:
- Simplifying the expression:
\[ N = \frac{33 + 18}{1} + 1 = \frac{51}{1} + 1 = 51 + 1 = 52 \]

6. **Conclusion**:
- Therefore, the total number of terms from -18 to 33, inclusive, is **52**.