Certainly! Let's analyze the given pattern step-by-step to find the missing number.
Given pattern: [tex]\(2, 4, 7, 11, 16\)[/tex]
1. Identify the Differences Between Consecutive Terms:
- The difference between the 2nd term and the 1st term: [tex]\(4 - 2 = 2\)[/tex]
- The difference between the 3rd term and the 2nd term: [tex]\(7 - 4 = 3\)[/tex]
- The difference between the 4th term and the 3rd term: [tex]\(11 - 7 = 4\)[/tex]
- The difference between the 5th term and the 4th term: [tex]\(16 - 11 = 5\)[/tex]
2. Observe the Pattern in Differences:
- The differences are: [tex]\(2, 3, 4, 5\)[/tex]
3. Predict the Next Difference:
- The pattern in the differences is increasing by 1 each time.
4. Calculate the Next Difference:
- The next difference, following the pattern, should be [tex]\(5 + 1 = 6\)[/tex].
5. Find the Missing Number:
- Add the next difference to the last term in the pattern.
- Last term in the pattern: [tex]\(16\)[/tex]
- Next difference: [tex]\(6\)[/tex]
- Therefore, the next term: [tex]\(16 + 6 = 22\)[/tex]
So the missing number in the pattern [tex]\(2, 4, 7, 11, 16, \square\)[/tex] is [tex]\(\boxed{22}\)[/tex].
