The ninth term of the sequence 0, 3, 8, 15, 24, 35, .... is

Options

A. 63
B. 70
C. 80
D. 99

Answer

To find the ninth term of the sequence 0, 3, 8, 15, 24, 35, we will first identify the pattern in the sequence.

1. **List the given terms:**
- The sequence is: 0, 3, 8, 15, 24, 35.

2. **Calculate the differences between consecutive terms:**
- 3 - 0 = 3
- 8 - 3 = 5
- 15 - 8 = 7
- 24 - 15 = 9
- 35 - 24 = 11

So, the first differences are: 3, 5, 7, 9, 11.

3. **Calculate the differences of the first differences (second differences):**
- 5 - 3 = 2
- 7 - 5 = 2
- 9 - 7 = 2
- 11 - 9 = 2

The second differences are constant and equal to 2.

4. **Identify the pattern in the first differences:**
- The first differences are increasing by 2 each time. Therefore, we can predict the next two first differences:
- After 11, the next difference will be 13 (11 + 2).
- After 13, the next difference will be 15 (13 + 2).

5. **Calculate the next terms in the sequence:**
- The seventh term:
- 35 + 13 = 48 (this is the seventh term).
- The eighth term:
- 48 + 15 = 63 (this is the eighth term).
- The ninth term:
- 63 + 17 = 80 (this is the ninth term).

6. **Final answer:**
- The ninth term of the sequence is **80**.