Sequences / Skips

The given sequence is $1113, 1112, 1111$.

Let's analyze the sequence:

• The first term is $1113$.
• The second term is $1112$, which is $1113 - 1$.
• The third term is $1111$, which is $1112 - 1$.

It's evident that each term is decreasing by $1$ from the previous term. Therefore, this sequence is an arithmetic sequence with a common difference of $-1$.

Given this information, we can continue the sequence by subtracting 1 from the last given term, $1111$.

• The next term is $1111 - 1 = 1110$.
• Following that, $1110 - 1 = 1109$.
• Finally, $1109 - 1 = 1108$.

Thus, the next three terms in the sequence are $1110, 1109,$ and $1108$.

Looking at the provided options, choice 4: $1110, 1109, 1108$, is the correct continuation of the sequence.

To complete the given sequence $36, 34, \ldots$, we need to identify the pattern in the sequence. From the given terms, it appears that the sequence is decreasing.

Let's check if this is an arithmetic sequence, where each term decreases by a constant amount:

• Subtract the second term from the first term: $36 - 34 = 2$.
• This indicates that each term is decreasing by 2.

Recognizing this pattern, the sequence can be continued by subtracting 2 from each subsequent term:

• The next term after 34 is calculated as follows: $34 - 2 = 32$.
• Continuing, the term after 32 is: $32 - 2 = 30$.
• Finally, the term following 30 is: $30 - 2 = 28$.

Therefore, the complete sequence is $36, 34, 32, 30, 28$.

The correct answer choice, which matches this sequence, is:

$36,34,32,30,28$

To complete the sequence $20{,}155, 20{,}154, 20{,}153, \ldots$, follow these steps:

• Step 1: Identify the sequence pattern.
• Step 2: Notice that each term decreases by 1 from the previous term.
• Step 3: Continue the pattern by subtracting 1 from the last known term.

Let's work through the steps:

Step 1:
The sequence given is: $20{,}155, 20{,}154, 20{,}153, \ldots$.
Step 2:
Observe that the first term $20{,}155$ is reduced to $20{,}154$, then to $20{,}153$, establishing a pattern of subtracting 1.
Step 3:
Using this pattern, find the next terms:
From $20{,}153$, subtract 1 to get $20{,}152$.
From $20{,}152$, subtract 1 to get $20{,}151$.
From $20{,}151$, subtract 1 to get $20{,}150$.

Therefore, the sequence continues as follows: $20{,}152, 20{,}151, 20{,}150$.

To solve the problem of completing the sequence $20, \ldots, 24, 26, \ldots, \ldots$, we recognize the sequence's underlying pattern.

Step 1: Analyze known terms.
The given sequence begins with $20, \ldots, 24, 26, \ldots, \ldots$. Notice the known terms $20$ and $24$, and $26$.

Step 2: Determine the difference between known terms.
The difference between $24$ and $20$ is $4$, suggesting an ongoing pattern.
Between $26$ and $24$, the difference is $2$, proposing alternation in differences or a complete oversight of interspersed terms around $26$.

Step 3: Determine full sequence consistency.
Check if numbers align with a two-step even-number sequence, which implies adding $2$ successively.
Extending forward and back confirms $20, 22, 24, 26, 28, \ldots$.

Step 4: Verification considering other instructions.
The sequence appears to be a straightforward arithmetic one comprising purely even numbers beginning from $20$. This step requires confirming subsequent numbers $28, 30$.

Conclusion: Sequential confirmation proves the arithmetic nature of the understanding, yielding:

$20,22,24,26,28,30$

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

• Step 1: Determine the common difference by looking at the known terms, 21 and 19.
• Step 2: Apply the common difference to find the missing terms in the sequence.
• Step 3: Verify the sequence pattern to ensure accuracy.

Now, let's work through each step:

Step 1: The common difference between 21 and 19 is 2. Thus, each number in the sequence is reduced by 2 from the previous one.

Step 2: Starting from 25, subtract 2 to fill in the first gap: $25 - 2 = 23$. Now the sequence is 25, 23, ..., 21, 19.

From 19, subtract 2 to fill in the next gap: $19 - 2 = 17$, then $17 - 2 = 15$. Thus, the complete sequence is:

$25, 23, 21, 19, 17, 15$

Therefore, the solution to the problem is $25, 23, 21, 19, 17, 15$.