What will come in place of question mark (?) in the following number series'
9 20 42 75 119 ?

Options

A. 174
B. 170
C. 168
D. 180

Answer

To find the number that comes in place of the question mark (?) in the series 9, 20, 42, 75, 119, we will analyze the differences between the consecutive terms and look for a pattern.

### Step 1: Identify the differences between consecutive terms
- The first term is 9.
- The second term is 20.
- The difference between the first and second term:
\( 20 - 9 = 11 \)

- The third term is 42.
- The difference between the second and third term:
\( 42 - 20 = 22 \)

- The fourth term is 75.
- The difference between the third and fourth term:
\( 75 - 42 = 33 \)

- The fifth term is 119.
- The difference between the fourth and fifth term:
\( 119 - 75 = 44 \)

So, the differences are:
- 11, 22, 33, 44

### Step 2: Identify the pattern in the differences
We can see that the differences are increasing by 11 each time:
- 11 (1st difference)
- 22 (2nd difference)
- 33 (3rd difference)
- 44 (4th difference)

### Step 3: Calculate the next difference
Following the pattern, the next difference should be:
- \( 44 + 11 = 55 \)

### Step 4: Add the next difference to the last term
Now, we add this difference to the last term in the series:
- Last term: 119
- Next difference: 55

Calculating the next term:
- \( 119 + 55 = 174 \)

### Conclusion
Thus, the number that comes in place of the question mark (?) is **174**.