Find a pattern in the sequence. Use the pattern to show the next two terms.1, 3, 7, 15, 31, ___ , ___
Question
Find a pattern in the sequence.
Use the pattern to show the next two terms.
Given sequence:
1, 3, 7, 15, 31, ___ , ___
Solution
The pattern in this sequence is that each term is one less than a power of 2.
1 is 2^0, 3 is 2^2 - 1, 7 is 2^3 - 1, 15 is 2^4 - 1, 31 is 2^5 - 1.
Following this pattern, the next term would be 2^6 - 1, which is 63. The term after that would be 2^7 - 1, which is 127.
So, the next two terms in the sequence are 63 and 127.
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