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2 votes
1, 3, 7, 15, 31, _, _, _
Describe the pattern.

User Dako
by
9.3k points

1 Answer

3 votes

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.

User Dharmvir Tiwari
by
8.6k points

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