What will come in place of question mark(?) in the following number series?
1462 1486 1510 ? 1558 1582

Options

A. 1525
B. 1520
C. 1534
D. 1524

Answer

To find the missing term in the number series: 1462, 1486, 1510, ?, 1558, 1582, we will follow these steps:

### Step 1: Identify the series
The given series is:
- 1462
- 1486
- 1510
- ?
- 1558
- 1582

### Step 2: Calculate the differences between consecutive terms
Let's calculate the differences between the consecutive terms:
- Difference between 1462 and 1486:
\[ 1486 - 1462 = 24 \]
- Difference between 1486 and 1510:
\[ 1510 - 1486 = 24 \]
- Difference between 1510 and the missing term (?):
\[ ? - 1510 = x \quad (we will find x) \]
- Difference between the missing term (?) and 1558:
\[ 1558 - ? = y \quad (we will find y) \]
- Difference between 1558 and 1582:
\[ 1582 - 1558 = 24 \]

### Step 3: Establish the pattern
From the differences we calculated, we can see that the difference between each consecutive term is consistently 24. Therefore, we can assume that the difference between the missing term and the previous term (1510) should also be 24.

### Step 4: Calculate the missing term
Using the established pattern:
\[ ? = 1510 + 24 = 1534 \]

### Step 5: Verify with the next term
Now, let's verify if the next term (1558) follows the same pattern:
- Difference between 1534 and 1558:
\[ 1558 - 1534 = 24 \]
This confirms that our calculation is correct.

### Conclusion
The missing term in the series is:
\[ \boxed{1534} \]

---