Sequences / Skips up to 100: Consecutive numbers

Examples with solutions for Sequences / Skips up to 100: Consecutive numbers

Exercise #1

Complete the sequence:

176,175,174, 176,175,174,\ldots

Step-by-Step Solution

To solve this problem, let's follow these steps:

  • Step 1: Identify the pattern in the given sequence.
  • Step 2: Recognize that the sequence decreases each term by 1.
  • Step 3: Continue subtracting 1 from each term to extend the sequence.

Now, let's perform each step:

Step 1: The given sequence is 176,175,174 176, 175, 174 . Observing these numbers, each term is exactly 1 less than the previous term.

Step 2: We can confirm the pattern is subtracting 1 from the preceding term.

Step 3: Continue this pattern with subsequent terms:

  • After 174, the next term is 1741=173 174 - 1 = 173 .
  • After 173, the next term is 1731=172 173 - 1 = 172 .
  • After 172, the next term is 1721=171 172 - 1 = 171 .
  • After 171, the next term is 1711=170 171 - 1 = 170 .

Therefore, by following the identified pattern, we extend the sequence as 173,172,171,170 173, 172, 171, 170 .

The correct answer is 173,172,171,170\mathbf{173, 172, 171, 170}.

Answer

173,172,171,170 173,172,171,170

Exercise #2

Complete the sequence:

107,108,109, 107,108,109,\ldots

Step-by-Step Solution

To solve this problem, we'll identify that we are dealing with an arithmetic sequence where each term increases by 1.

  • Step 1: Identify the pattern in the sequence.
  • Step 2: Note that the difference between consecutive terms is 1.
  • Step 3: Extend the sequence from the last given term.

Now, let's work through these steps:

Step 1: The sequence starts at 107,108,109 107, 108, 109 . The difference is clearly 1, as each number is 1 more than its predecessor.

Step 2: The rule for this sequence is to take the last number and add 1 to generate the next number. We continue the pattern.

Step 3: Continuing from 109:

  • 109 + 1 = 110
  • 110 + 1 = 111
  • 111 + 1 = 112
  • 112 + 1 = 113

Therefore, the next numbers in the sequence are 110,111,112,113 110, 111, 112, 113 .

Hence, the correct answer choice is the one with the sequence 110,111,112,113 110, 111, 112, 113 .

Answer

110,111,112,113 110,111,112,113

Exercise #3

Complete the sequence:

450,451,452, 450,451,452,\ldots

Step-by-Step Solution

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

  • Step 1: Recognize the sequence pattern. Here, we have consecutive numbers: 450, 451, 452, where each number increases by 1.
  • Step 2: Identify the last given number in the sequence, which is 452.
  • Step 3: Continue the sequence by adding 1 to the last given number to find the next three numbers.

Let's work through these steps:
Step 1: The sequence is clearly a series of consecutive numbers.
Step 2: The last given number is 452452.
Step 3: Continuing from 452452, the next number is 452+1=453452 + 1 = 453.
Similarly, the next number after that is 453+1=454453 + 1 = 454, and the next number after that is 454+1=455454 + 1 = 455.

The numbers that come after 450,451,452450, 451, 452 in this sequence are: 453,454,455 453, 454, 455 .

Answer

453,454,455 453,454,455