3 219 344 408 ? 443 444

Options

A. 416
B. 435
C. 423
D. 428

Explanation

To solve the series: 3, 219, 344, 408, ?, 443, 444, we will analyze the differences between consecutive terms.

### Step-by-Step Solution:

1. **Identify the first term and the second term:**
- First term (T1) = 3
- Second term (T2) = 219

2. **Calculate the difference between the first and second terms:**
- Difference (D1) = T2 - T1 = 219 - 3 = 216
- Note: 216 = 6³ (cube of 6)

3. **Identify the second and third terms:**
- Third term (T3) = 344

4. **Calculate the difference between the second and third terms:**
- Difference (D2) = T3 - T2 = 344 - 219 = 125
- Note: 125 = 5³ (cube of 5)

5. **Identify the third and fourth terms:**
- Fourth term (T4) = 408

6. **Calculate the difference between the third and fourth terms:**
- Difference (D3) = T4 - T3 = 408 - 344 = 64
- Note: 64 = 4³ (cube of 4)

7. **Determine the next difference for the unknown term (?):**
- The pattern seems to be that the differences are cubes of decreasing integers: 6³, 5³, 4³.
- The next difference should be 3³ = 27.

8. **Calculate the unknown term (?):**
- Let the unknown term be X.
- Since the next term after the unknown term is 443, we can express this as:
- X + 27 = 443
- Therefore, X = 443 - 27 = 416.

9. **Final series with the unknown term filled in:**
- The complete series is: 3, 219, 344, 408, 416, 443, 444.

### Conclusion:
The value of the question mark (?) is **416**.