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

Question 4

Step 1: Recall the formula for the \(n^{th}\) term of an AP:

\(a_n = a + (n-1)\,d\)

Here, \(a\) = first term, \(d\) = common difference, and \(n\) = term number.

Step 2: From the given AP \(-5, -\tfrac{5}{2}, 0, \tfrac{5}{2}, \ldots\)

First term, \(a = -5\).

Common difference, \(d = -\tfrac{5}{2} - (-5) = -\tfrac{5}{2} + 5 = \tfrac{5}{2}.\)

Step 3: We want the 11th term, so \(n = 11\).

Using the formula: \(a_{11} = a + (11-1)\,d\)

\(a_{11} = -5 + 10 \times \tfrac{5}{2}\)

Step 4: Simplify:

\(10 \times \tfrac{5}{2} = 25\)

So, \(a_{11} = -5 + 25 = 20\).

Final Answer: The 11th term is 20. Option B.