NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 5: Arithematic Progressions - Exercise 5.1

Question 9

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