Complete the Sequence: An Arithmetic Progression with Million Multiples

Question

Complete the sequence:

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

Step-by-Step Solution

To solve this problem, we will follow these steps:

  • Step 1: Identify the pattern by examining the given numbers in the sequence.
  • Step 2: Calculate the difference between the first two numbers in the sequence.
  • Step 3: Use this difference to find the next numbers in the sequence.

Now, let's work through each step:

Step 1: The given sequence starts with the numbers 1,000,0001,000,000 and 2,000,0002,000,000.

Step 2: We calculate the difference between these numbers: 2,000,0001,000,000=1,000,000 2,000,000 - 1,000,000 = 1,000,000 This suggests that each term in the sequence increases by 1,000,0001,000,000.

Step 3: Using this pattern, we add 1,000,0001,000,000 to the last known term to find the next terms: 2,000,000+1,000,000=3,000,000 2,000,000 + 1,000,000 = 3,000,000 3,000,000+1,000,000=4,000,000 3,000,000 + 1,000,000 = 4,000,000 4,000,000+1,000,000=5,000,000 4,000,000 + 1,000,000 = 5,000,000 Thus, the next terms in the sequence are 3,000,0003,000,000, 4,000,0004,000,000, and 5,000,0005,000,000.

Therefore, the solution to the problem is:
3,000,000, 4,000,000, 5,000,0003{,}000{,}000,\ 4{,}000{,}000,\ 5{,}000{,}000.

Answer

3,000,000, 4,000,000, 5,000,000 3{,}000{,}000,\ 4{,}000{,}000, \ 5{,}000{,}000


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