What will come in place of question mark (?) in the following number series?
28, 37, 64, 109, 172, (?)

Options

A. 253
B. 265
C. 234
D. 246

Answer

To find the missing number in the series 28, 37, 64, 109, 172, (?), we will analyze the differences between consecutive terms.

### Step 1: Calculate the differences between consecutive terms
- Difference between 28 and 37:
\( 37 - 28 = 9 \)

- Difference between 37 and 64:
\( 64 - 37 = 27 \)

- Difference between 64 and 109:
\( 109 - 64 = 45 \)

- Difference between 109 and 172:
\( 172 - 109 = 63 \)

So, the differences we have so far are:
9, 27, 45, 63.

### Step 2: Calculate the differences of the differences
Now, let's find the differences of these differences:
- Difference between 9 and 27:
\( 27 - 9 = 18 \)

- Difference between 27 and 45:
\( 45 - 27 = 18 \)

- Difference between 45 and 63:
\( 63 - 45 = 18 \)

The second-level differences are all 18.

### Step 3: Find the next difference
Since the second-level difference is constant (18), we can find the next first-level difference by adding 18 to the last first-level difference:
- Next difference:
\( 63 + 18 = 81 \)

### Step 4: Calculate the next term in the series
Now, we add this difference to the last term in the original series:
- Next term:
\( 172 + 81 = 253 \)

Thus, the missing number in the series is **253**.

### Final Answer:
The value that comes in place of the question mark (?) is **253**.

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