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Which recursive formula can be used to define this sequence for ?Choices:(A)(B)(C)(D)
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Q. Which recursive formula can be used to define this sequence for ?Choices:(A)(B)(C)(D)
- Analyze Sequence: Analyze the sequence to determine if it is arithmetic or geometric.The sequence given is To determine if it is arithmetic or geometric, we look at the differences or ratios between terms.
- Calculate Differences: Calculate the difference between consecutive terms to see if it is constant, which would indicate an arithmetic sequence.The difference between the first two terms is .The difference between the second and third terms is .Since the difference is constant, we can conclude that the sequence is arithmetic with a common difference of .
- Formulate Recursive Formula: Formulate the recursive formula for an arithmetic sequence. For an arithmetic sequence, the recursive formula is generally , where is the common difference. Since we have determined that the common difference is , the recursive formula becomes .
- Match with Choices: Match the recursive formula with the given choices.The correct recursive formula is .Looking at the choices provided:(A) (Incorrect, does not make sense mathematically)(B) (Incorrect, does not make sense mathematically)(C) (Incorrect, implies a geometric sequence)(D) (Incorrect notation, but the right side of the equation matches our formula)The correct choice is (D), but the notation should be .
