Find the next term of series: 0, 3, 8, 15, 24, ?

Question

Accepted Answer

To determine the next term in the series 0, 3, 8, 15, 24, we need to identify the pattern or rule governing the sequence. Let's analyze the differences between consecutive terms:

- The difference between the 1st term (0) and the 2nd term (3) is 3.
- The difference between the 2nd term (3) and the 3rd term (8) is 5.
- The difference between the 3rd term (8) and the 4th term (15) is 7.
- The difference between the 4th term (15) and the 5th term (24) is 9.

We observe that the differences between consecutive terms are increasing by 2 each time: 3, 5, 7, 9. This suggests that the differences form an arithmetic sequence with a common difference of 2.

Following this pattern, the next difference should be 11 (9 + 2). Therefore, to find the next term in the series, we add this difference to the last term:

24 (last term) + 11 (next difference) = 35

Thus, the next term in the series is 35, which corresponds to Option 3.

Now, let's explain why the other options are incorrect:

1. **Option 1: 33** - This option is incorrect because it does not follow the established pattern of differences. The difference from 24 to 33 is 9, which does not continue the arithmetic sequence of differences (3, 5, 7, 9, 11).

2. **Option 2: 34** - This option is incorrect for the same reason as Option 1. The difference from 24 to 34 is 10, which does not fit the pattern of increasing differences by 2.

3. **Option 4: 36** - This option is incorrect because the difference from 24 to 36 is 12, which again does not follow the arithmetic sequence of differences (3, 5, 7, 9, 11).

In conclusion, Option 3 (35) is the correct answer as it adheres to the logical pattern of the series.