-4, 8, -16, 32
arithmetic 64, 128, 256
geometric -64, 128, -256
Geometric -48, 64, -80
the sequence is neither geometric nor arithmetic
Is it b?
miss sue?
damn all the way in 2013 and you never got answered
To determine whether a sequence is arithmetic or geometric, we need to examine the pattern of the numbers.
An arithmetic sequence is one in which there is a common difference between each pair of consecutive terms. In other words, by adding or subtracting the same value to each term, we obtain the next term.
A geometric sequence, on the other hand, is one in which there is a common ratio between each pair of consecutive terms. By multiplying or dividing the same value to each term, we obtain the next term.
Let's break down each sequence:
Sequence 1: -4, 8, -16, 32
To check if it is arithmetic, we need to see if there is a common difference between each pair of consecutive terms. Take the difference between each term: 8 - (-4) = 12, -16 - 8 = -24, and 32 - (-16) = 48. As the differences are not the same, this sequence is not arithmetic.
To check if it is geometric, we need to see if there is a common ratio between each pair of consecutive terms. Take the ratio between each term: 8 / (-4) = -2, -16 / 8 = -2, and 32 / (-16) = -2. As the ratios are the same (-2), this sequence is geometric.
Sequence 2: 64, 128, 256
To check if it is arithmetic, we need to see if there is a common difference between each pair of consecutive terms. Take the difference between each term: 128 - 64 = 64 and 256 - 128 = 128. As the differences are not the same, this sequence is not arithmetic.
To check if it is geometric, we need to see if there is a common ratio between each pair of consecutive terms. Take the ratio between each term: 128 / 64 = 2 and 256 / 128 = 2. As the ratios are the same (2), this sequence is geometric.
Sequence 3: -64, 128, -256
To check if it is arithmetic, we need to see if there is a common difference between each pair of consecutive terms. Take the difference between each term: 128 - (-64) = 192 and (-256) - 128 = -384. As the differences are not the same, this sequence is not arithmetic.
To check if it is geometric, we need to see if there is a common ratio between each pair of consecutive terms. Take the ratio between each term: 128 / (-64) = -2 and (-256) / 128 = -2. As the ratios are the same (-2), this sequence is geometric.
Sequence 4: -48, 64, -80
To check if it is arithmetic, we need to see if there is a common difference between each pair of consecutive terms. Take the difference between each term: 64 - (-48) = 112 and (-80) - 64 = -144. As the differences are not the same, this sequence is not arithmetic.
To check if it is geometric, we need to see if there is a common ratio between each pair of consecutive terms. Take the ratio between each term: 64 / (-48) = -4/3 and (-80) / 64 = -5/4. As the ratios are not the same, this sequence is not geometric.
Conclusion:
Based on the analysis above, only the second sequence (64, 128, 256) is geometric, while the rest are neither geometric nor arithmetic.