लुप्त पद ज्ञात करें : `2,9,28,65,?`

Options

A. 121
B. 195
C. 126
D. 103

Answer

To find the missing term in the sequence `2, 9, 28, 65, ?`, we can analyze the pattern in the sequence. Let's break it down step by step:

### Step 1: Identify the Pattern
We will look for a pattern in the given numbers. The numbers are:
- 2
- 9
- 28
- 65

### Step 2: Find the Differences
Let's find the differences between consecutive terms:
- 9 - 2 = 7
- 28 - 9 = 19
- 65 - 28 = 37

So, the differences are:
- 7
- 19
- 37

### Step 3: Find the Differences of Differences
Now, let's find the differences of these differences:
- 19 - 7 = 12
- 37 - 19 = 18

So, the second level of differences is:
- 12
- 18

### Step 4: Find the Differences of the Second Level
Next, we find the difference of the second level:
- 18 - 12 = 6

This indicates that the second level of differences is increasing by 6.

### Step 5: Continue the Pattern
If we continue this pattern, the next difference in the second level will be:
- 18 + 6 = 24

### Step 6: Find the Next First Level Difference
Now, we add this to the last first level difference:
- 37 + 24 = 61

### Step 7: Find the Next Term
Finally, we add this difference to the last term in the original sequence:
- 65 + 61 = 126

### Conclusion
Thus, the missing term in the sequence is **126**.