Which recursive formula can be used to define this sequence for n 1? 15, 13, 11, 9, 7, 5, ... Choices: [[an = an - 1 - 2][an = an - 1 + an - 2 + 2][an = 13/15an - 1][an = -1/2an - 1]]

Question

Which recursive formula can be used to define this sequence for n > 1?      15, 13, 11, 9, 7, 5, ...          Choices: [[an = an - 1 - 2][an = an - 1 + an - 2 + 2][an = 13/15an - 1][an = -1/2an - 1]]

Bytelearn · Accepted Answer

Determine sequence type: We need to determine if the sequence is arithmetic, geometric, or neither. To do this, we look at the differences or ratios between terms.Calculate difference between first two terms: The sequence given is 15, 13, 11, 9, 7, 5, .... We calculate the difference between the first two terms: 13 - 15 = -2.Check consistency of difference: We check if this difference is consistent by calculating the difference between the next two terms: 11 - 13 = -2.Conclude arithmetic sequence: Since the difference between each pair of consecutive terms is the same, we conclude that the sequence is arithmetic with a common difference of -2.Find recursive formula: Now we need to find a recursive formula that represents this arithmetic sequence. The recursive formula for an arithmetic sequence is generally given by an = an-1 + d, where d is the common difference.Substitute common difference: Substituting the common difference we found into the recursive formula, we get an = an-1 - 2.Compare with given choices: We compare our derived formula with the given choices. The correct recursive formula that matches our derived formula is an = an-1 - 2.

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