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Sagot :
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.
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.
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