Classify the sequence left-brace a subscript n baseline right-brace equals left-brace 3 comma negative 1 comma Start Fraction 1 over 3 End Fraction comma negative Start Fraction 1 over 9 End Fraction ellipsis right-brace as arithmetic, geometric, or neither. If there is not enough information to classify the sequence, choose not enough information.

Answer 1

To classify the sequence, we need to determine if there is a common difference between consecutive terms or a common ratio between consecutive terms.

The given sequence is: {a_n} = {3, -1, 1/3, -1/9, ...}

To check if it is an arithmetic sequence, we need to see if there is a common difference between consecutive terms. Let's calculate the differences:
-1 - 3 = -4
1/3 - (-1) = 4/3
-1/9 - (1/3) = -4/9

The differences are not constant, so the sequence is not arithmetic.

To check if it is a geometric sequence, we need to see if there is a common ratio between consecutive terms. Let's calculate the ratios:
-1 / 3 = -1/3
1/3 / (-1) = -1/3
-1/9 / (1/3) = -1/3

The ratios are constant, so the sequence is geometric.

Therefore, the given sequence {a_n} = {3, -1, 1/3, -1/9, ...} is a geometric sequence.