What will come in place of question mark (? ) in the following number series ?
`7 " "8 " "24 " "105" "361" "?`

Options

A. 986
B. 617
C. 486
D. 1657

Answer

To solve the number series: 7, ?, 8, ?, 24, ?, 105, ?, 361, ?, ?

We need to identify the pattern in the series.

### Step 1: Identify the differences between the numbers
- From 7 to 8: The difference is 1.
- From 8 to 24: The difference is 16.
- From 24 to 105: The difference is 81.
- From 105 to 361: The difference is 256.

### Step 2: Recognize the pattern in the differences
- The differences we have are: 1, 16, 81, 256.
- These numbers are perfect squares:
- 1 = 1²
- 16 = 4²
- 81 = 9²
- 256 = 16²

### Step 3: Identify the pattern in the square numbers
- The squares are increasing by the squares of consecutive integers:
- 1² (1)
- 2² (4)
- 3² (9)
- 4² (16)

### Step 4: Determine the next square
- The next square in the pattern is 5², which equals 25.

### Step 5: Calculate the next number in the series
- To find the next number after 361, we add 625 (which is 25²) to 361:
- 361 + 625 = 986

### Conclusion
The number that comes in place of the question mark (?) in the series is **986**.

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