What will come in the place of question mark (?) in the following number sereis:
`4," "3," "4," "9," "32," "?`

Options

A. A)75
B. B)155
C. C)125
D. D)175

Answer

To find the missing term in the series `4, 3, 4, 9, 32, ?`, we will analyze the pattern of the series step by step.

### Step 1: Identify the pattern
The series is:
- 1st term: 4
- 2nd term: 3
- 3rd term: 4
- 4th term: 9
- 5th term: 32

Let's denote the terms as \( a_1, a_2, a_3, a_4, a_5 \):
- \( a_1 = 4 \)
- \( a_2 = 3 \)
- \( a_3 = 4 \)
- \( a_4 = 9 \)
- \( a_5 = 32 \)

### Step 2: Analyze the relationship between terms
1. From \( a_1 \) to \( a_2 \):
\[ a_2 = a_1 - 1 \cdot 1 = 4 - 1 = 3 \]

2. From \( a_2 \) to \( a_3 \):
\[ a_3 = a_2 - 1 \cdot 2 = 3 + 1 = 4 \]

3. From \( a_3 \) to \( a_4 \):
\[ a_4 = a_3 \cdot 3 - 3 = 4 \cdot 3 - 3 = 12 - 3 = 9 \]

4. From \( a_4 \) to \( a_5 \):
\[ a_5 = a_4 \cdot 4 - 4 = 9 \cdot 4 - 4 = 36 - 4 = 32 \]

### Step 3: Find the next term \( a_6 \)
Now, we will apply the same pattern to find \( a_6 \):
\[ a_6 = a_5 \cdot 5 - 5 = 32 \cdot 5 - 5 \]
Calculating this:
\[ 32 \cdot 5 = 160 \]
So,
\[ a_6 = 160 - 5 = 155 \]

### Conclusion
The missing term in the series is **155**.