Find the `16^(th)` term of the AP: 2, 7, 12, 17, …… .

Answer

To find the 16th term of the arithmetic progression (AP) given by the series 2, 7, 12, 17, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the first term (A) and the common difference (D)**:
- The first term \( A \) is the first number in the series, which is \( 2 \).
- The common difference \( D \) is calculated by subtracting the first term from the second term:
\[ D = A_2 - A_1 = 7 - 2 = 5 \]

2. **Use the formula for the nth term of an AP**:
- The formula for the nth term \( A_n \) of an arithmetic progression is given by:
\[ A_n = A + (n - 1) \cdot D \]
- Here, we need to find the 16th term, so we set \( n = 16 \).

3. **Substitute the values into the formula**:
- Substitute \( A = 2 \), \( n = 16 \), and \( D = 5 \) into the formula:
\[ A_{16} = 2 + (16 - 1) \cdot 5 \]

4. **Calculate the value**:
- First, calculate \( 16 - 1 \):
\[ 16 - 1 = 15 \]
- Then, multiply by the common difference \( D \):
\[ 15 \cdot 5 = 75 \]
- Finally, add this to the first term \( A \):
\[ A_{16} = 2 + 75 = 77 \]

5. **Conclusion**:
- The 16th term of the AP is \( 77 \).

### Final Answer:
The 16th term of the AP is \( 77 \).