Question

which sequence is not an arithmetic sequence? 12, 18, 24, 30,... 10, 3, -4, -11,... 16, 20, 24, 28,... 2, 4, 8, 16,...

Explanation:

To determine which sequence is not an arithmetic sequence, we check the common difference between consecutive terms. An arithmetic sequence has a constant common difference \(d = a_{n + 1}-a_n\) for all \(n\).

Step 1: Analyze the first sequence (12, 18, 24, 30,...)

Calculate the differences:
\(18 - 12 = 6\)
\(24 - 18 = 6\)
\(30 - 24 = 6\)
The common difference \(d = 6\) (constant), so it is an arithmetic sequence.

Step 2: Analyze the second sequence (10, 3, -4, -11,...)

Calculate the differences:
\(3 - 10 = -7\)
\(-4 - 3 = -7\)
\(-11 - (-4)= -7\)
The common difference \(d = -7\) (constant), so it is an arithmetic sequence.

Step 3: Analyze the third sequence (16, 20, 24, 28,...)

Calculate the differences:
\(20 - 16 = 4\)
\(24 - 20 = 4\)
\(28 - 24 = 4\)
The common difference \(d = 4\) (constant), so it is an arithmetic sequence.

Step 4: Analyze the fourth sequence (2, 4, 8, 16,...)

Calculate the differences:
\(4 - 2 = 2\)
\(8 - 4 = 4\)
\(16 - 8 = 8\)
The differences are \(2, 4, 8\), which are not constant. So this sequence is not an arithmetic sequence.

Answer:

The sequence \(2, 4, 8, 16, \dots\) is not an arithmetic sequence.