The next number of the sequence 2,6, 12, 20, 30, 42, 56. — Is

Options

A. 60
B. 64
C. 70
D. 72

Answer

To find the next number in the sequence 2, 6, 12, 20, 30, 42, 56, we can follow these steps:

### Step 1: Identify the Sequence
The given sequence is:
2, 6, 12, 20, 30, 42, 56.

### Step 2: Calculate the Differences Between Consecutive Terms
Let's find the differences between each pair of consecutive terms:
- 6 - 2 = 4
- 12 - 6 = 6
- 20 - 12 = 8
- 30 - 20 = 10
- 42 - 30 = 12
- 56 - 42 = 14

So, the differences are:
4, 6, 8, 10, 12, 14.

### Step 3: Identify the Pattern in the Differences
The differences themselves form a sequence:
4, 6, 8, 10, 12, 14.

We can see that these differences increase by 2 each time.

### Step 4: Determine the Next Difference
Following the pattern, the next difference after 14 would be:
14 + 2 = 16.

### Step 5: Add the Next Difference to the Last Term
Now, we add this next difference to the last term in the original sequence:
56 + 16 = 72.

### Conclusion
Thus, the next number in the sequence is **72**.

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