20th term of the A.P. `-10, -6, -2, 2,..........` is :

Options

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

Answer

To find the 20th term of the arithmetic progression (A.P.) given by the sequence -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 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 of an A.P.**:
The formula for the nth term (Tn) of an A.P. is:
\[ T_n = A + (n - 1) \cdot d \]
Here, we need to find the 20th term (n = 20).

4. **Substitute the values into the formula**:
Substitute A, d, and n into the formula:
\[ T_{20} = -10 + (20 - 1) \cdot 4 \]

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

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

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

### Final Answer:
The 20th term of the A.P. is:
\[ T_{20} = 66 \]