The 11th term of the AP \(-5,\; -\dfrac{5}{2},\; 0,\; \dfrac{5}{2},\ldots\) is
−20
20
−30
30
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.