Q. What kind of sequence is this?37,56,75,94,…Choices:(A) arithmetic(B) geometric(C) both(D) neither
Verify Consecutive Differences: Let's verify if the differences between consecutive terms are uniform. Given sequence: 37,56,75,94,…Are the consecutive differences in the sequence equal? 56−37=19, 75−56=19, 94−75=19.The consecutive differences in the sequence are equal.
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.
Check for Geometric Sequence: Now, let's check if the sequence could also be geometric by finding the ratios between consecutive terms. 3756 does not yield a whole number, and neither does 5675 nor 7594. This indicates that there is no common ratio, and therefore, the sequence is not geometric.
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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