In series 359,365,371,`"……….."`, what will be the 10th term ?

Answer

To find the 10th term of the series 359, 365, 371, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Series**:
The given series is 359, 365, 371, ...

2. **Determine the Common Difference**:
- To find the common difference (d), subtract the first term from the second term:
- \( d = 365 - 359 = 6 \)
- Verify with the next terms:
- \( 371 - 365 = 6 \)
- Thus, the common difference \( d = 6 \).

3. **Identify the First Term**:
- The first term \( a_1 \) is 359.

4. **Use the Formula for the n-th Term of an Arithmetic Progression (AP)**:
- The formula for the n-th term \( a_n \) of an AP is:
\[ a_n = a_1 + (n - 1) \cdot d \]
- Here, we need to find the 10th term, so \( n = 10 \).

5. **Substitute Values into the Formula**:
- Substitute \( a_1 = 359 \), \( n = 10 \), and \( d = 6 \) into the formula:
\[ a_{10} = 359 + (10 - 1) \cdot 6 \]

6. **Calculate**:
- First, calculate \( (10 - 1) \cdot 6 \):
\[ 9 \cdot 6 = 54 \]
- Now, substitute back into the equation:
\[ a_{10} = 359 + 54 \]
- Finally, add:
\[ a_{10} = 413 \]

### Final Answer:
The 10th term of the series is **413**.

---