Which recursive formula can be used to define this sequence for n > 1?15,22,29,36,43,50,…Choices:(A) an=an−1+7(B) an=1522an−1(C) an=an−1+an−1−7(D) an=an−1+an−1+7
Q. Which recursive formula can be used to define this sequence for n>1?15,22,29,36,43,50,…Choices:(A) an=an−1+7(B) an=1522an−1(C) an=an−1+an−1−7(D) an=an−1+an−1+7
Sequence Type: We have the sequence: 15,22,29,36,43,50,…Is the given sequence geometric or arithmetic?The difference between consecutive terms appears to be constant.The given sequence is likely arithmetic.
Calculate Differences: To confirm that the sequence is arithmetic, we calculate the difference between consecutive terms.The difference between the first two terms is 22−15=7.The difference between the second and third terms is 29−22=7.Since the difference is the same, the sequence is indeed arithmetic with a common difference of 7.
Identify Recursive Formula: Now, we need to identify the recursive formula for the given arithmetic sequence.The recursive formula for an arithmetic sequence is generally an=an−1+d, where d is the common difference.In this case, d=7.Therefore, the recursive formula is an=an−1+7.
Match with Choices: We match our recursive formula with the given choices.The correct choice that represents the recursive formula an=an−1+7 is:(A) a=a+7However, this choice is not correctly written. It should be an=an−1+7, not just a=a+7.
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