Let's examine the given sequence: 3, 4, 6, 9, 13, 18, 24.
To find the next number in this sequence, we need to identify the pattern of differences between consecutive terms.
First, let's determine the differences:
- The difference between the 1st term (3) and the 2nd term (4) is [tex]\(4 - 3 = 1\)[/tex].
- The difference between the 2nd term (4) and the 3rd term (6) is [tex]\(6 - 4 = 2\)[/tex].
- The difference between the 3rd term (6) and the 4th term (9) is [tex]\(9 - 6 = 3\)[/tex].
- The difference between the 4th term (9) and the 5th term (13) is [tex]\(13 - 9 = 4\)[/tex].
- The difference between the 5th term (13) and the 6th term (18) is [tex]\(18 - 13 = 5\)[/tex].
- The difference between the 6th term (18) and the 7th term (24) is [tex]\(24 - 18 = 6\)[/tex].
We can observe that the differences between consecutive terms are increasing by 1 each time:
1, 2, 3, 4, 5, 6.
To find the next number in the sequence, we add the next difference to the last term. The next difference should be [tex]\(6 + 1 = 7\)[/tex].
So, we add 7 to the last term (24):
[tex]\[24 + 7 = 31\][/tex]
Therefore, the next number in the sequence is 31.
