165,195,255,285,345(….)

Options

A. 375
B. 420
C. 435
D. 390

Answer

To find the next term in the series 165, 195, 255, 285, 345, we can analyze the pattern in the numbers.

### Step-by-Step Solution:

1. **Identify the Pattern**:
The series consists of numbers that can be expressed as the product of 15 and certain prime numbers.

2. **List the Terms**:
- 165 = 15 × 11
- 195 = 15 × 13
- 255 = 15 × 17
- 285 = 15 × 19
- 345 = 15 × 23

3. **Identify the Prime Numbers**:
The prime numbers being multiplied by 15 are: 11, 13, 17, 19, 23.

4. **Find the Next Prime Number**:
The next prime number after 23 is 29.

5. **Calculate the Next Term**:
To find the next term in the series, multiply 15 by the next prime number:
- Next term = 15 × 29 = 435.

6. **Conclusion**:
Therefore, the next term in the series is **435**.