5, 10, 19, 36, 69, ….

Options

A. 128
B. 129
C. 132
D. 134

Explanation

To find the next number in the series: 5, 10, 19, 36, 69, we will analyze the pattern step by step.

### Step 1: Identify the pattern
Let's look at the differences between consecutive terms:
- From 5 to 10: \(10 - 5 = 5\)
- From 10 to 19: \(19 - 10 = 9\)
- From 19 to 36: \(36 - 19 = 17\)
- From 36 to 69: \(69 - 36 = 33\)

So, the differences are: 5, 9, 17, 33.

### Step 2: Analyze the differences
Now, let's look at the differences of the differences:
- From 5 to 9: \(9 - 5 = 4\)
- From 9 to 17: \(17 - 9 = 8\)
- From 17 to 33: \(33 - 17 = 16\)

The second differences are: 4, 8, 16.

### Step 3: Identify the pattern in the second differences
The second differences are doubling each time:
- \(4 \times 2 = 8\)
- \(8 \times 2 = 16\)

Following this pattern, the next second difference would be:
- \(16 \times 2 = 32\)

### Step 4: Calculate the next first difference
Now, we can add this to the last first difference:
- Last first difference is 33.
- Next first difference = \(33 + 32 = 65\)

### Step 5: Calculate the next term in the series
Now, we add this new first difference to the last term in the series:
- Last term is 69.
- Next term = \(69 + 65 = 134\)

### Conclusion
Thus, the next number in the series is **134**.