Which number will replace the '?' in the following sequence ?
`5, 7, 14, 24, 42, ?, 119 `

Options

A. 71
B. 67
C. 65
D. 63

Answer

To find the number that will replace the '?' in the sequence `5, 7, 14, 24, 42, ?, 119`, we can analyze the pattern in the sequence step by step.

### Step 1: Identify the sequence
The sequence given is:
- 5
- 7
- 14
- 24
- 42
- ?
- 119

### Step 2: Look for a pattern
Let's examine the differences between consecutive terms:
- 7 - 5 = 2
- 14 - 7 = 7
- 24 - 14 = 10
- 42 - 24 = 18

So the differences are:
- 2, 7, 10, 18

### Step 3: Analyze the differences
Now, let's look at the differences of the differences:
- 7 - 2 = 5
- 10 - 7 = 3
- 18 - 10 = 8

The second differences are:
- 5, 3, 8

### Step 4: Identify a new approach
The differences do not show a clear pattern. Let's try to see if we can generate the next term by adding the previous two terms starting from the third term:
- 5 + 7 = 12 (not used)
- 7 + 14 = 21 (not used)
- 14 + 24 = 38 (not used)
- 24 + 42 = 66 (not used)

### Step 5: Calculate the next term
Now, we will add the last two terms:
- 24 + 42 = 66

### Step 6: Add the next increment
Now, we need to add a certain increment to this sum. Observing the pattern, we can see that the increments appear to increase:
- The last increment was 5 (from 66).

So, we will add 5 to 66:
- 66 + 5 = 71

### Step 7: Verify the next term
Now, let's check if this fits with the next term in the sequence:
- The next term should be 119.
- 42 + 71 = 113
- Now add the next increment, which appears to be 6:
- 113 + 6 = 119

### Conclusion
Thus, the number that will replace the '?' in the sequence is **71**.