What will come in place of question mark (?) in the following series questions?
1,2,10,37,101,?

Options

A. 225
B. 227
C. 226
D. 220

Answer

To solve the series 1, 2, 10, 37, 101, ?, we need to identify the pattern in the sequence. Let's break it down step by step.

### Step 1: Identify the Pattern
We start by looking at the differences between consecutive terms in the series.

- From 1 to 2: \(2 - 1 = 1\)
- From 2 to 10: \(10 - 2 = 8\)
- From 10 to 37: \(37 - 10 = 27\)
- From 37 to 101: \(101 - 37 = 64\)

So, the differences between the terms are:
1, 8, 27, 64

### Step 2: Analyze the Differences
Next, we can observe that these differences are actually cubes of consecutive integers:
- \(1 = 1^3\)
- \(8 = 2^3\)
- \(27 = 3^3\)
- \(64 = 4^3\)

### Step 3: Predict the Next Difference
Following this pattern, the next difference should be \(5^3\):
- \(5^3 = 125\)

### Step 4: Calculate the Next Term
Now, we add this difference to the last term in the series:
- \(101 + 125 = 226\)

### Conclusion
Thus, the next term in the series is **226**.

### Final Answer
The number that will come in place of the question mark (?) is **226**.

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