What will come in place of question mark (?) in the following series questions?
1,2,6,15,?

Options

A. A)31
B. B)30
C. C)25
D. D)40

Answer

To find the missing term in the series 1, 2, 6, 15, ?, we can analyze the pattern of the series step by step.

### Step 1: Identify the series
The series given is:
1, 2, 6, 15, ?

### Step 2: Find the differences between consecutive terms
Let's calculate the differences between consecutive terms:
- From 1 to 2: \(2 - 1 = 1\)
- From 2 to 6: \(6 - 2 = 4\)
- From 6 to 15: \(15 - 6 = 9\)

So, the differences are:
1, 4, 9

### Step 3: Analyze the differences
Now, let's look at the differences we calculated:
- The first difference is \(1\) (which is \(1^2\))
- The second difference is \(4\) (which is \(2^2\))
- The third difference is \(9\) (which is \(3^2\))

### Step 4: Identify the pattern in the differences
We can see that the differences are perfect squares:
- The first difference corresponds to \(1^2\)
- The second difference corresponds to \(2^2\)
- The third difference corresponds to \(3^2\)

### Step 5: Calculate the next difference
Following the pattern, the next difference should be \(4^2\):
- \(4^2 = 16\)

### Step 6: Add the next difference to the last term
Now, we add this difference to the last known term in the series:
- Last term is \(15\)
- Next difference is \(16\)

So, we calculate:
\[ 15 + 16 = 31 \]

### Conclusion
The missing term in the series is \(31\).

### Final Answer
Thus, the answer is \(31\).

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