If the common difference of an AP is 5, then what is `a_(18)-a_(13)` ?

Options

A. 5
B. 20
C. 25
D. 30

Explanation

To solve the problem of finding \( a_{18} - a_{13} \) when the common difference \( d \) of an arithmetic progression (AP) is 5, we can follow these steps:

### Step 1: Write the formula for the nth term of an AP
The nth term of an arithmetic progression can be expressed using the formula:
\[ a_n = a + (n - 1) \cdot d \]
where:
- \( a_n \) is the nth term,
- \( a \) is the first term,
- \( n \) is the term number,
- \( d \) is the common difference.

### Step 2: Calculate \( a_{18} \)
Using the formula for the 18th term:
\[ a_{18} = a + (18 - 1) \cdot d = a + 17 \cdot d \]
Substituting \( d = 5 \):
\[ a_{18} = a + 17 \cdot 5 = a + 85 \]

### Step 3: Calculate \( a_{13} \)
Now, using the formula for the 13th term:
\[ a_{13} = a + (13 - 1) \cdot d = a + 12 \cdot d \]
Substituting \( d = 5 \):
\[ a_{13} = a + 12 \cdot 5 = a + 60 \]

### Step 4: Find \( a_{18} - a_{13} \)
Now, we can find the difference:
\[ a_{18} - a_{13} = (a + 85) - (a + 60) \]
Simplifying this expression:
\[ a_{18} - a_{13} = a + 85 - a - 60 = 85 - 60 = 25 \]

### Final Answer
Thus, the value of \( a_{18} - a_{13} \) is:
\[ \boxed{25} \]