What will come in place of question mark (?) in the following sereis questions?
9,10,18,27,91,?

Options

A. A)100
B. B)144
C. C)125
D. D)116

Answer

To solve the series: 9, 10, 18, 27, 91, ?, we will analyze the pattern of the numbers step by step.

### Step 1: Identify the differences between consecutive terms.
- From 9 to 10: \(10 - 9 = 1\)
- From 10 to 18: \(18 - 10 = 8\)
- From 18 to 27: \(27 - 18 = 9\)
- From 27 to 91: \(91 - 27 = 64\)

### Step 2: List the differences.
The differences we found are:
- 1, 8, 9, 64

### Step 3: Analyze the differences.
Now, let's see if these differences have a pattern:
- The first difference is \(1 = 1^2\) (1 squared)
- The second difference is \(8 = 2^3\) (2 cubed)
- The third difference is \(9 = 3^2\) (3 squared)
- The fourth difference is \(64 = 4^3\) (4 cubed)

### Step 4: Identify the pattern in the differences.
The pattern alternates between squares and cubes:
- 1st term: \(1^2\)
- 2nd term: \(2^3\)
- 3rd term: \(3^2\)
- 4th term: \(4^3\)

Following this pattern, the next difference should be \(5^2\):
- \(5^2 = 25\)

### Step 5: Calculate the missing term.
Now, we add this difference to the last known term (91):
- \(91 + 25 = 116\)

### Conclusion:
The missing term in the series is \(116\).

### Final Answer:
The value that comes in place of the question mark (?) is **116**.