What is the seventh term of the sequence 0,3,8,15,24 ?

Options

A. 63
B. 48
C. 35
D. 33

Answer

To find the seventh term of the sequence 0, 3, 8, 15, 24, we will analyze the differences between the terms and identify a pattern.

### Step 1: Write down the sequence
The given sequence is:
- 0, 3, 8, 15, 24

### Step 2: Calculate the differences between consecutive terms
Let's find the differences between each pair of consecutive terms:
- 3 - 0 = 3
- 8 - 3 = 5
- 15 - 8 = 7
- 24 - 15 = 9

So, the differences are:
- 3, 5, 7, 9

### Step 3: Identify the pattern in the differences
The differences we found (3, 5, 7, 9) are consecutive odd numbers. The next odd number after 9 is 11.

### Step 4: Calculate the sixth term
To find the sixth term, we add the next odd number (11) to the last term of the sequence (24):
- 24 + 11 = 35

### Step 5: Calculate the seventh term
Now, to find the seventh term, we add the next odd number (13) to the sixth term (35):
- 35 + 13 = 48

### Conclusion
The seventh term of the sequence is 48.

### Final Answer
The seventh term is **48**.

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