What value will come in place of question mark(?) in the number series given below?
37, 46, 73, 118, 181 ?

Options

A. 260
B. 258
C. 262
D. 264

Answer

To find the value that will come in place of the question mark (?) in the number series 37, 46, 73, 118, 181, we can follow these steps:

### Step 1: Identify the differences between consecutive terms
We will calculate the differences between each pair of consecutive numbers in the series.

- Difference between 46 and 37:
\( 46 - 37 = 9 \)

- Difference between 73 and 46:
\( 73 - 46 = 27 \)

- Difference between 118 and 73:
\( 118 - 73 = 45 \)

- Difference between 181 and 118:
\( 181 - 118 = 63 \)

So the differences are:
9, 27, 45, 63.

### Step 2: Identify the pattern in the differences
Now, we will look at the differences we calculated:
- 9
- 27
- 45
- 63

Next, we will find the differences between these differences to see if there is a pattern:
- Difference between 27 and 9:
\( 27 - 9 = 18 \)

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

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

The second differences are all 18, which indicates that the first differences are increasing by a constant value of 18.

### Step 3: Calculate the next difference
Since the last difference we calculated is 63, we can find the next difference by adding 18 to it:
- Next difference:
\( 63 + 18 = 81 \)

### Step 4: Calculate the next term in the series
Now, we will add this next difference (81) to the last term in the series (181) to find the next term:
- Next term:
\( 181 + 81 = 262 \)

Thus, the value that will come in place of the question mark (?) is **262**.

### Summary of the Solution:
The next term in the series is 262.

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