Find the next number in the series. 4, 9, 20, 43, ?

Options

A. 100
B. 92
C. 82
D. 90

Answer

To find the next number in the series 4, 9, 20, 43, we will analyze the pattern step by step.

### Step 1: Identify the pattern
We start with the numbers in the series: 4, 9, 20, 43. We need to find a relationship between these numbers.

### Step 2: Find the differences
Let's calculate the differences between consecutive terms:
- 9 - 4 = 5
- 20 - 9 = 11
- 43 - 20 = 23

So, the differences are: 5, 11, 23.

### Step 3: Analyze the differences
Next, we look at the differences of the differences:
- 11 - 5 = 6
- 23 - 11 = 12

The second differences are: 6, 12.

### Step 4: Find the pattern in the second differences
Now, let's find the differences of the second differences:
- 12 - 6 = 6

The third difference is constant (6), which suggests that the differences are increasing in a quadratic manner.

### Step 5: Predict the next difference
Since the last second difference is 12, we can add 6 to it to find the next second difference:
- Next second difference = 12 + 6 = 18.

### Step 6: Calculate the next first difference
Now, we can add this new second difference to the last first difference:
- Next first difference = 23 + 18 = 41.

### Step 7: Calculate the next term in the series
Finally, we add this new first difference to the last term in the series:
- Next term = 43 + 41 = 84.

### Conclusion
Thus, the next number in the series is **84**.

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