Q. What kind of sequence is this?429,429,429,429,…Choices:(A) arithmetic(B) geometric(C) both(D) neither
Arithmetic Sequence Definition: An arithmetic sequence is a sequence of numbers with the difference between any two consecutive terms being constant. This difference is called the common difference.To check if the given sequence is arithmetic, we calculate the difference between consecutive terms.Difference = 429−429=0
Check for Arithmetic Sequence: Since the difference between consecutive terms is constant (0 in this case), the sequence is an arithmetic sequence.
Geometric Sequence Definition: A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.To check if the given sequence is geometric, we calculate the ratio between consecutive terms.Ratio = 429429=1
Check for Geometric Sequence: Since the ratio between consecutive terms is constant (1 in this case), the sequence is also a geometric sequence.
Conclusion: The given sequence is both an arithmetic sequence (with a common difference of 0) and a geometric sequence (with a common ratio of 1).