Answer: 63, 127, 255
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Step-by-step explanation
The gap between terms are: 2, 4, 8, 16
The scratch work is shown below
- 3-1 = 2
- 7-3 = 4
- 15-7 = 8
- 31-15 = 16
The sequence 2,4,8,16 is the powers of 2. The general term is of the form 2^n where n is an integer {1,2,3,4,...}
If this pattern keeps up, then the next gap is 2^5 = 32, so the next term would be 31+32 = 63
The next gap after that would be 2^6 = 64 which leads to the next term being 63+64 = 127
The last gap needed is 2^7 = 128 and it gives the last term as 127+128 = 255
The sequence extends to 1, 3, 7, 15, 31, 63, 127, 255
One thing to notice: Each term is one less than a power of 2.
So as a shortcut, we could use the formula (2^n) - 1 to generate each term.