Complete the series 0,2,3,5,8,10,15,17,24,26.... A. 35 B. 32 C. 30 D. 28 E. 25

To complete the series, let's try to identify a pattern in the given numbers. It appears that the series alternates between two different sequences.

First, let's look at the odd-indexed terms (1st, 3rd, 5th, 7th, etc.):

1st term: 0
3rd term: 3 (3 = 0 + 3)
5th term: 8 (8 = 5 + 3)
7th term: 15 (15 = 8 + 7)
9th term: 24 (24 = 15 + 9)

Now, let's look at the even-indexed terms (2nd, 4th, 6th, 8th, etc.):

2nd term: 2
4th term: 5 (5 = 2 + 3)
6th term: 10 (10 = 5 + 5)
8th term: 17 (17 = 10 + 7)
10th term: 26 (26 = 17 + 9)

From this analysis, we can see that the odd-indexed terms form an arithmetic sequence with a common difference of increasing consecutive positive integers (1, 2, 3, 4, ...), and the even-indexed terms form an arithmetic sequence with a common difference of 3.

To find the next term in the series, we need to add the next number from both sequences:

Next odd-indexed term: 24 + 11 = 35
Next even-indexed term: 26 + 3 = 29

So, the next term in the series should be 35. None of the provided options matches this answer. Please double-check the options or the series itself.