The `11 ^(th)` term of the `A.P.:-5,- (5)/(2), 0, (5)/(2),...` is

Options

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

Answer

To find the 11th term of the arithmetic progression (A.P.) given by the sequence -5, -5/2, 0, 5/2, ..., we will follow these steps:

### Step 1: Identify the first term (a) and the common difference (d)
- The first term \( a \) is the first number in the sequence, which is:
\[ a = -5 \]

- To find the common difference \( d \), we subtract the first term from the second term:
\[ d = a_2 - a_1 = -\frac{5}{2} - (-5) \]
Simplifying this gives:
\[ d = -\frac{5}{2} + 5 = -\frac{5}{2} + \frac{10}{2} = \frac{5}{2} \]

### Step 2: Use the formula for the nth term of an A.P.
The formula for the nth term \( a_n \) of an A.P. is given by:
\[ a_n = a + (n - 1) \cdot d \]
We need to find the 11th term \( a_{11} \):
\[ a_{11} = a + (11 - 1) \cdot d \]
Substituting the values of \( a \) and \( d \):
\[ a_{11} = -5 + (10) \cdot \frac{5}{2} \]

### Step 3: Calculate \( a_{11} \)
Calculating \( (10) \cdot \frac{5}{2} \):
\[ 10 \cdot \frac{5}{2} = \frac{50}{2} = 25 \]
Now substituting back into the equation for \( a_{11} \):
\[ a_{11} = -5 + 25 = 20 \]

### Conclusion
Thus, the 11th term of the A.P. is:
\[ \boxed{20} \]

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