If the common difference of an AP is 5, then what is \(a_{18}-a_{13}\)?
5
20
25
30
We are asked to find \(a_{18} - a_{13}\), which means the difference between the 18th term and the 13th term of an Arithmetic Progression (AP).
Step 1: Recall the property of AP. The difference between the \(m\)-th term and the \(n\)-th term is given by:
\(a_m - a_n = (m - n) \times d\)
Here, \(d\) is the common difference.
Step 2: In this question, \(m = 18\), \(n = 13\), and \(d = 5\).
Step 3: Substitute the values:
\(a_{18} - a_{13} = (18 - 13) \times 5\)
Step 4: Simplify the bracket:
\(18 - 13 = 5\)
Step 5: Multiply:
\(5 \times 5 = 25\)
So, \(a_{18} - a_{13} = 25\).
Correct option: C