The next term of the series
4, 7, 11, 18, 29, ....... is:

Options

A. 47
B. 45
C. 40
D. 36

Answer

To find the next term in the series 4, 7, 11, 18, 29, we will analyze the differences between the terms step by step.

### Step 1: Identify the terms in the series
The given series is:
- First term (T1) = 4
- Second term (T2) = 7
- Third term (T3) = 11
- Fourth term (T4) = 18
- Fifth term (T5) = 29

### Step 2: Calculate the differences between consecutive terms
Now, we will find the difference between each pair of consecutive terms:
- T2 - T1 = 7 - 4 = 3
- T3 - T2 = 11 - 7 = 4
- T4 - T3 = 18 - 11 = 7
- T5 - T4 = 29 - 18 = 11

So, the differences are:
- 3, 4, 7, 11

### Step 3: Calculate the differences of the differences
Next, we will find the differences of these differences:
- 4 - 3 = 1
- 7 - 4 = 3
- 11 - 7 = 4

So, the second differences are:
- 1, 3, 4

### Step 4: Calculate the differences of the second differences
Now, we will find the differences of the second differences:
- 3 - 1 = 2
- 4 - 3 = 1

So, the third differences are:
- 2, 1

### Step 5: Identify the pattern
From the differences calculated, we can see that the differences are increasing. The last difference we calculated was 4. If we continue this pattern, we can add the last difference (which is 4) to the last term of the first differences (which is 11).

### Step 6: Calculate the next difference
Next difference = 11 + 4 = 15

### Step 7: Calculate the next term
Now, we will add this difference to the last term of the original series:
Next term = 29 + 15 = 44

### Conclusion
Therefore, the next term in the series is **44**.

---