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For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence). 5,1,-3,dots -4 (1)/(5) 4 5

For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).\newline5,1,−3,… 5,1,-3, \ldots \newline−4 -4 \newline15 \frac{1}{5} \newline44\newline55

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Q. For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).\newline5,1,−3,… 5,1,-3, \ldots \newline−4 -4 \newline15 \frac{1}{5} \newline44\newline55
  1. Check Differences: To determine if the sequence is arithmetic or geometric, we need to check the differences or ratios between terms.\newlineFirst, we check the difference between the first and second term: 1−5=−41 - 5 = -4.
  2. Identify Arithmetic Sequence: Next, we check the difference between the second and third term: −3−1=−4-3 - 1 = -4.
  3. Compare Common Difference: Since the differences between consecutive terms are the same, the sequence is an arithmetic sequence with a common difference of −4-4.
  4. Match Given Options: Now we compare the common difference to the given options to identify the correct one.\newlineThe common difference we found is −4-4, which matches one of the given options.

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