The 11th term of an AP -5, `(-5)/(2)`, 0, `(5)/(2)`, …

Options

A. -20
B. 20
C. -30
D. 30

Explanation

To find the 11th term of the given arithmetic progression (AP) -5, -5/2, 0, 5/2, ..., we can use the formula for the nth term of an AP:

**Step 1: Identify the first term (a) and the common difference (d).**
- The first term \( a \) is -5.
- To find the common difference \( d \), we can subtract the first term from the second term:
\[ d = -\frac{5}{2} - (-5) = -\frac{5}{2} + 5 = -\frac{5}{2} + \frac{10}{2} = \frac{5}{2} \]

**Step 2: Use the formula for the nth term of an AP.**
- The formula for the nth term \( A_n \) is given by:
\[ A_n = a + (n - 1) \cdot d \]
- Here, we need to find the 11th term, so \( n = 11 \).

**Step 3: Substitute the values into the formula.**
- Substitute \( a = -5 \), \( n = 11 \), and \( d = \frac{5}{2} \) into the formula:
\[ A_{11} = -5 + (11 - 1) \cdot \frac{5}{2} \]
\[ A_{11} = -5 + 10 \cdot \frac{5}{2} \]
\[ A_{11} = -5 + 25 \]

**Step 4: Calculate the final result.**
- Now, simplify the expression:
\[ A_{11} = -5 + 25 = 20 \]

Thus, the 11th term of the AP is **20**.