What will come in place of question mark (?) in the following series questions?
20,24,32,?,60,80

Options

A. A)40
B. B)44
C. C)48
D. D)52

Answer

To solve the series: 20, 24, 32, ?, 60, 80, we need to identify the pattern in the series.

### Step-by-Step Solution:

1. **Identify the first few terms and their differences:**
- The first term is 20.
- The second term is 24.
- The third term is 32.
- The fifth term is 60.
- The sixth term is 80.

2. **Calculate the differences between consecutive terms:**
- From 20 to 24:
\[ 24 - 20 = 4 \]
- From 24 to 32:
\[ 32 - 24 = 8 \]
- From 32 to the unknown term (let's call it \( k \)):
\[ k - 32 \]
- From \( k \) to 60:
\[ 60 - k \]
- From 60 to 80:
\[ 80 - 60 = 20 \]

3. **List the differences:**
- The differences we have so far are:
- 4 (from 20 to 24)
- 8 (from 24 to 32)
- \( k - 32 \) (from 32 to \( k \))
- \( 60 - k \) (from \( k \) to 60)
- 20 (from 60 to 80)

4. **Look for a pattern in the differences:**
- The differences are increasing: 4, 8, ?, 20.
- Notice that the differences seem to be multiples of 4:
- 4 (which is \( 4 \times 1 \))
- 8 (which is \( 4 \times 2 \))
- The next difference should be \( 4 \times 3 = 12 \).
- The difference after that is \( 20 \) (which is \( 4 \times 5 \)).

5. **Set up the equations based on the pattern:**
- From 32 to \( k \):
\[ k - 32 = 12 \implies k = 32 + 12 = 44 \]
- From \( k \) to 60:
\[ 60 - k = 16 \implies k = 60 - 16 = 44 \]

6. **Conclusion:**
- The value of \( k \) is 44.

Thus, the missing term in the series is **44**.