Which term of the A.P. 1,4,7,10,…….. Is 52?

Answer

To find which term of the arithmetic progression (A.P.) 1, 4, 7, 10, ... is equal to 52, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the first term (a) and the common difference (d)**:
- The first term \( a = 1 \).
- The common difference \( d = 4 - 1 = 3 \).

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 \( n \) such that \( a_n = 52 \).

3. **Set up the equation**:
- Substitute \( a = 1 \), \( d = 3 \), and \( a_n = 52 \) into the formula:
\[ 52 = 1 + (n - 1) \cdot 3 \]

4. **Simplify the equation**:
- Rearranging gives:
\[ 52 - 1 = (n - 1) \cdot 3 \]
\[ 51 = (n - 1) \cdot 3 \]

5. **Solve for \( n - 1 \)**:
- Divide both sides by 3:
\[ n - 1 = \frac{51}{3} \]
\[ n - 1 = 17 \]

6. **Find \( n \)**:
- Add 1 to both sides:
\[ n = 17 + 1 = 18 \]

7. **Conclusion**:
- Thus, the 18th term of the A.P. is 52.

### Final Answer:
The term of the A.P. that is equal to 52 is the **18th term**.