Complete the Sequence: Finding the Next Term After 1113, 1112, 1111

Question

Complete the sequence:

1,113, 1,112, 1,111,  1{,}113,\ 1{,}112,\ 1{,}111, \ \ldots

Step-by-Step Solution

The given sequence is 1113,1112,1111 1113, 1112, 1111 .

Let's analyze the sequence:

  • The first term is 1113 1113 .
  • The second term is 1112 1112 , which is 11131 1113 - 1 .
  • The third term is 1111 1111 , which is 11121 1112 - 1 .

It's evident that each term is decreasing by 1 1 from the previous term. Therefore, this sequence is an arithmetic sequence with a common difference of 1-1.

Given this information, we can continue the sequence by subtracting 1 from the last given term, 1111 1111 .

  • The next term is 11111=1110 1111 - 1 = 1110 .
  • Following that, 11101=1109 1110 - 1 = 1109 .
  • Finally, 11091=1108 1109 - 1 = 1108 .

Thus, the next three terms in the sequence are 1110,1109, 1110, 1109, and 1108 1108 .

Looking at the provided options, choice 4: 1110,1109,1108 1110, 1109, 1108 , is the correct continuation of the sequence.

Answer

1,110, 1,109, 1,108 1{,}110,\ 1{,}109,\ 1{,}108


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