Complete the Sequence: Finding the Pattern in 1,000, 2,000, 3,000,...

Question

Complete the sequence:

1,000, 2,000, 3,000,  1{,}000,\ 2{,}000,\ 3{,}000, \ \ldots

Step-by-Step Solution

To solve this problem, let's determine the pattern in the given sequence:

  • Given Sequence: 1000,2000,3000, 1000, 2000, 3000, \ldots
  • Step 1: Calculate the common difference.
    • The difference between 2000 and 1000 is 20001000=1000 2000 - 1000 = 1000 .
    • The difference between 3000 and 2000 is 30002000=1000 3000 - 2000 = 1000 .
  • Step 2: Use the common difference to find the subsequent terms.
    • The next term after 3000 is 3000+1000=4000 3000 + 1000 = 4000 .
    • Following that, the next term is 4000+1000=5000 4000 + 1000 = 5000 .
    • And then 5000+1000=6000 5000 + 1000 = 6000 .
  • Step 3: Compare with answer choices.
  • Choice 4: 4000,5000,6000 4000, 5000, 6000 matches the calculated sequence.

Therefore, the completed sequence is 4000,5000,6000 4000, 5000, 6000 .

Answer

4,000, 5,000, 6,000 4{,}000,\ 5{,}000,\ 6{,}000


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