Sequences / Skips up to a million: Jumps of 10,000

Examples with solutions for Sequences / Skips up to a million: Jumps of 10,000

Exercise #1

Complete the sequence:

380,000, 370,000,  380{,}000,\ 370{,}000, \ \ldots

Step-by-Step Solution

To solve this problem, we'll determine the pattern in the sequence and extend it:

  • Step 1: Identify the pattern in the sequence
  • Step 2: Calculate the common difference
  • Step 3: Use the common difference to extend the sequence

Now, let's work through each step:
Step 1: The sequence starts with 380,000 380{,}000 and 370,000 370{,}000 . By observation, the numbers are decreasing.
Step 2: Calculate the common difference: 370,000380,000=10,000 370{,}000 - 380{,}000 = -10{,}000 . This tells us the sequence decreases by 10,000 10{,}000 for each step.
Step 3: Continue the sequence using the common difference:

  • The next term after 370,000 370{,}000 is 370,00010,000=360,000 370{,}000 - 10{,}000 = 360{,}000 .
  • The following term is 360,00010,000=350,000 360{,}000 - 10{,}000 = 350{,}000 .
  • The term after that is 350,00010,000=340,000 350{,}000 - 10{,}000 = 340{,}000 .

Therefore, the completed sequence is: 360,000, 350,000, 340,000 360{,}000,\ 350{,}000, \ 340{,}000 .

Answer

360,000, 350,000, 340,000 360{,}000,\ 350{,}000, \ 340{,}000

Exercise #2

Complete the sequence:

200,000, 210,000,  200{,}000,\ 210{,}000, \ \ldots

Step-by-Step Solution

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

  • Step 1: Identify the difference between the given terms.
  • Step 2: Use this difference to calculate subsequent terms.

Now, let's proceed with these steps:
Step 1: The given terms are 200,000 and 210,000. The difference between these terms is 210,000200,000=10,000 210,000 - 200,000 = 10,000 .

Step 2: Assuming this sequence follows an arithmetic pattern, the common difference is 10,000 10,000 . Therefore, each subsequent number is the previous number plus 10,000 10,000 .

Let's find the next few terms:

  • The term after 210,000 is 210,000+10,000=220,000 210,000 + 10,000 = 220,000 .
  • The subsequent term is 220,000+10,000=230,000 220,000 + 10,000 = 230,000 .
  • The next term is 230,000+10,000=240,000 230,000 + 10,000 = 240,000 .

Therefore, the complete sequence is 200,000,210,000,220,000,230,000,240,000 200,000, 210,000, 220,000, 230,000, 240,000 .

The correct answer choice is: 220,000,230,000,240,000 220,000, 230,000, 240,000 , which matches option 3.

Answer

220,000, 230,000, 240,000 220{,}000,\ 230{,}000, \ 240{,}000