Complete the following sequence:
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Complete the following sequence:
To solve the problem of completing the sequence , we recognize the sequence's underlying pattern.
Step 1: Analyze known terms.
The given sequence begins with . Notice the known terms and , and .
Step 2: Determine the difference between known terms.
The difference between and is , suggesting an ongoing pattern.
Between and , the difference is , proposing alternation in differences or a complete oversight of interspersed terms around .
Step 3: Determine full sequence consistency.
Check if numbers align with a two-step even-number sequence, which implies adding successively.
Extending forward and back confirms .
Step 4: Verification considering other instructions.
The sequence appears to be a straightforward arithmetic one comprising purely even numbers beginning from . This step requires confirming subsequent numbers .
Conclusion: Sequential confirmation proves the arithmetic nature of the understanding, yielding:
Complete the following sequence:
\( 20,\ldots,24,26\ldots ,\ldots \)
The key is recognizing this is a sequence of consecutive even numbers! The gap between 20 and 24 skips 22, but the actual pattern is add 2 each time: 20, 22, 24, 26, 28, 30.
Look at the complete pattern first. Since we have even numbers with differences of 2, work backwards and forwards: 20 + 2 = 22, then 22 + 2 = 24, and so on.
Always use all given information! Here, 20, 24, 26 tells us it's consecutive evens, not jumps of 4. The missing 22 between 20 and 24 is the clue.
Verify that your sequence has a consistent pattern. For , each difference is 2, and all given terms (20, 24, 26) appear in the right positions.
While other mathematical patterns are possible, the most logical and simple completion is consecutive even numbers. This matches all given terms with the smallest, most consistent rule.
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