What value will come in place of question mark (?) in the series given below?
147, 144, 138, 126, 102, ?

Options

A. 52
B. 54
C. 56
D. 50

Answer

To find the value that will replace the question mark (?) in the series 147, 144, 138, 126, 102, we will analyze the differences between the consecutive terms.

1. **Identify the series**: The series given is 147, 144, 138, 126, 102.

2. **Calculate the differences**:
- From 147 to 144:
\[ 147 - 144 = 3 \]
- From 144 to 138:
\[ 144 - 138 = 6 \]
- From 138 to 126:
\[ 138 - 126 = 12 \]
- From 126 to 102:
\[ 126 - 102 = 24 \]

3. **List the differences**: The differences we calculated are:
- 3, 6, 12, 24.

4. **Observe the pattern in the differences**:
- The differences are increasing:
- 3 (which is \(3 \times 1\))
- 6 (which is \(3 \times 2\))
- 12 (which is \(3 \times 4\))
- 24 (which is \(3 \times 8\))

5. **Identify the next difference**:
- The pattern in the differences appears to be doubling each time:
- \(3, 6, 12, 24\) suggests the next difference should be \(3 \times 16 = 48\).

6. **Calculate the next term**:
- Now we subtract this next difference from the last term in the series:
\[ 102 - 48 = 54. \]

7. **Conclusion**:
- Therefore, the value that will come in place of the question mark (?) is **54**.