What comes next in the sequence: 1, 2, 6, 22, ...?
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Correct Answer: Option C
Explanation:
To find the next term in the sequence \(1, 2, 6, 22, \ldots\), let's identify the pattern:
1. Calculate the differences between consecutive terms:
- \(2 - 1 = 1\)
- \(6 - 2 = 4\)
- \(22 - 6 = 16\)
2. Notice that the differences \(1, 4, 16\) are \(2^0, 2^2, 2^4\) respectively.
3. The next difference should be \(2^6 = 64\).
4. Add this difference to the last term:
- \(22 + 64 = 86\)
So, the next term in the sequence is 86.
Thus, the correct answer is:
C. 86
To find the next term in the sequence \(1, 2, 6, 22, \ldots\), let's identify the pattern:
1. Calculate the differences between consecutive terms:
- \(2 - 1 = 1\)
- \(6 - 2 = 4\)
- \(22 - 6 = 16\)
2. Notice that the differences \(1, 4, 16\) are \(2^0, 2^2, 2^4\) respectively.
3. The next difference should be \(2^6 = 64\).
4. Add this difference to the last term:
- \(22 + 64 = 86\)
So, the next term in the sequence is 86.
Thus, the correct answer is:
C. 86