Sequences / Skips up to a million: Jumps of 1,000

Examples with solutions for Sequences / Skips up to a million: Jumps of 1,000

Exercise #1

Complete the sequence:

57,000, 58,000, 59,000,  57{,}000,\ 58{,}000,\ 59{,}000, \ \ldots

Step-by-Step Solution

To solve this problem, we'll analyze the pattern of the given sequence:

  • Step 1: Identify the pattern in the sequence.
  • Step 2: Calculate the common difference.
  • Step 3: Apply this pattern to find the next numbers.

Step 1: Examine the given sequence: 57,000,58,000,59,000 57,000, 58,000, 59,000 .

Step 2: The difference between consecutive terms is 58,00057,000=1,000 58,000 - 57,000 = 1,000 and 59,00058,000=1,000 59,000 - 58,000 = 1,000 . Therefore, the common difference is 1,000 1,000 .

Step 3: To find the next terms, add 1,000 1,000 to the last term:

  • Add 1,000 1,000 to 59,000 59,000 to get 60,000 60,000 .
  • Add 1,000 1,000 to 60,000 60,000 to get 61,000 61,000 .
  • Add 1,000 1,000 to 61,000 61,000 to get 62,000 62,000 .

Thus, the complete sequence is: 60,000,61,000,62,000 60,000, 61,000, 62,000 .

Therefore, the solution to the problem is: 60,000,61,000,62,000 60,000, 61,000, 62,000 .

Answer

60,000, 61,000, 62,000 60{,}000,\ 61{,}000,\ 62{,}000

Exercise #2

Complete the sequence:

715,347, 714,347,  715{,}347,\ 714{,}347, \ \ldots

Step-by-Step Solution

To solve the sequence problem, we follow these steps:

  • Step 1: Determine the pattern of the sequence by finding the common difference.
  • Step 2: Use the common difference to find the next terms.

Step 1: The first number in the sequence is 715,347, and the second is 714,347. Subtract the second from the first:
715,347714,347=1,000 715,347 - 714,347 = 1,000 .
This indicates that each term is 1,000 less than the previous term.

Step 2: To find the next numbers in the sequence, continue subtracting 1,000 from the last known term:
- Third term: 714,3471,000=713,347 714,347 - 1,000 = 713,347 .
- Fourth term: 713,3471,000=712,347 713,347 - 1,000 = 712,347 .
- Fifth term: 712,3471,000=711,347 712,347 - 1,000 = 711,347 .

Thus, the next three terms in the sequence are 713,347 713,347 , 712,347 712,347 , and 711,347 711,347 .

Therefore, the correct completion of the sequence is: 713,347,712,347,711,347 713,347, 712,347, 711,347 .

Answer

713,347, 712,347, 711,347 713{,}347,\ 712{,}347, \ 711{,}347

Exercise #3

Complete the sequence:

582,985, 583,985,  582{,}985,\ 583{,}985, \ \ldots

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the increment between the given sequence numbers.
  • Step 2: Use this increment to find the next numbers in the sequence.

Let's work through each step:

Step 1: Identify the increment.
The sequence begins with 582,985 582,985 and 583,985 583,985 . Calculate the difference between these numbers:
583,985582,985=1,000 583,985 - 582,985 = 1,000 .
Thus, each number in the sequence increases by 1,000.

Step 2: Extend the sequence.
Starting from the last given number 583,985 583,985 , add 1,000 to find the subsequent numbers:

  • The next number is 583,985+1,000=584,985 583,985 + 1,000 = 584,985 .
  • The following number is 584,985+1,000=585,985 584,985 + 1,000 = 585,985 .
  • Continue this process: 585,985+1,000=586,985 585,985 + 1,000 = 586,985 .

Therefore, by continuing the arithmetic pattern, the completed sequence is:
584,985,585,985,586,985 584,985, 585,985, 586,985 .

Matching this result with the given choices, the correct answer is choice 3, which is:
584,985,585,985,586,985 584,985, 585,985, 586,985 .

Answer

584,985, 585,985, 586,985 584{,}985,\ 585{,}985, \ 586{,}985