Identify the Sequence 1 , 2 , 4 , 6 , 8

Problem

1,2,4,6,8

Solution

1. Observe the terms of the given sequence: (a_1)=1 (a_2)=2 (a_3)=4 (a_4)=6 and (a_5)=8

2. Check for a common difference starting from the second term.

2−1=1

4−2=2

6−4=2

8−6=2

3. Identify the pattern. The sequence begins with 1 but every subsequent term increases by a constant difference of 2 This indicates that for n≥2 the sequence follows an arithmetic pattern.

4. Classify the sequence. Since the first term does not follow the constant difference established by the rest of the terms, this is a non-standard sequence. However, the terms 2, 4, 6, 8$ are the first four positive even integers.

Final Answer

1,2,4,6,8=A non-standard sequence where *(a_1)=1* and *(a_n)=2*(n−1)* for *n≥2

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