In an A.P. `-10, -6, -2, 2,……..20th` term is :

Options

A. 66
B. `-66`
C. `77`
D. None of these

Answer

To find the 20th term of the given arithmetic progression (A.P.) `-10, -6, -2, 2,...`, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the First Term (a)**:
The first term of the A.P. is given as:
\[ a = -10 \]

2. **Determine the Common Difference (d)**:
The common difference \(d\) can be calculated by subtracting the first term from the second term:
\[ d = -6 - (-10) = -6 + 10 = 4 \]

3. **Use the Formula for the nth Term**:
The formula for the nth term of an A.P. is given by:
\[ T_n = a + (n - 1) \cdot d \]
Here, we need to find the 20th term, so we set \(n = 20\).

4. **Substitute the Values into the Formula**:
Now, substitute \(a = -10\), \(d = 4\), and \(n = 20\) into the formula:
\[ T_{20} = -10 + (20 - 1) \cdot 4 \]

5. **Calculate (n - 1)**:
First, calculate \(20 - 1\):
\[ 20 - 1 = 19 \]

6. **Multiply by the Common Difference (d)**:
Now multiply \(19\) by \(4\):
\[ 19 \cdot 4 = 76 \]

7. **Add to the First Term (a)**:
Finally, add this result to the first term:
\[ T_{20} = -10 + 76 = 66 \]

Thus, the 20th term of the A.P. is:
\[ \boxed{66} \]