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What kind of sequence is this?\newline37,56,75,94,37, 56, 75, 94, \dots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither

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Q. What kind of sequence is this?\newline37,56,75,94,37, 56, 75, 94, \dots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither
  1. Verify Consecutive Differences: Let's verify if the differences between consecutive terms are uniform. Given sequence: 37,56,75,94,37, 56, 75, 94, \ldots\newlineAre the consecutive differences in the sequence equal? \newline5637=1956 - 37 = 19, 7556=1975 - 56 = 19, 9475=1994 - 75 = 19.\newlineThe consecutive differences in the sequence are equal.
  2. Identify Arithmetic Sequence: Since the consecutive differences are equal, this indicates that the sequence is an arithmetic sequence. An arithmetic sequence is defined by having a common difference between consecutive terms.
  3. Check for Geometric Sequence: Now, let's check if the sequence could also be geometric by finding the ratios between consecutive terms. 5637\frac{56}{37} does not yield a whole number, and neither does 7556\frac{75}{56} nor 9475\frac{94}{75}. This indicates that there is no common ratio, and therefore, the sequence is not geometric.
  4. Final Conclusion: Based on the previous steps, we can conclude that the sequence is arithmetic because it has a common difference, and it is not geometric because it does not have a common ratio.

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