Which recursive formula can be used to define this sequence for n 1? 1, 12, 23, 34, 45, 56, ... Choices: (A)a = a + 11 (B)a = a - 11 (C)a = 17/6a (D)a = a + a + 11

Question

Which recursive formula can be used to define this sequence for n > 1?   1, 12, 23, 34, 45, 56, ...    Choices: (A)a = a + 11 (B)a = a - 11 (C)a = 17/6a (D)a = a + a + 11

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Determine Pattern: We need to determine the pattern of the sequence to find the recursive formula. Let's look at the sequence: 1, 12, 23, 34, 45, 56, ... We can see that each term after the first increases by 11 from the previous term. This suggests that the sequence is arithmetic with a common difference of 11.Confirm Common Difference: To confirm the common difference, we calculate the difference between consecutive terms: 12 - 1 = 11 23 - 12 = 11 34 - 23 = 11 45 - 34 = 11 56 - 45 = 11 Since the difference is consistently 11, we can confirm that the sequence is arithmetic with a common difference of 11.Express Recursive Formula: Now, we need to express this pattern as a recursive formula. A recursive formula for an arithmetic sequence is generally of the form: a_n = a_(n-1) + d where a_n is the nth term, a_(n-1) is the previous term, and d is the common difference.Match with Choices: Substituting the common difference (d = 11) into the recursive formula, we get: a_n = a_(n-1) + 11 This formula will give us the next term in the sequence by adding 11 to the previous term.Now, let's match our recursive formula with the given choices: (A) a = a + 11 (This is incorrect; it lacks the subscript n to denote the nth term.) (B) a = a - 11 (This is incorrect; it suggests subtracting 11, which is not the pattern we found.) (C) a = 17/6a (This is incorrect; it suggests a geometric sequence with a ratio of 17/6, which is not the case.) (D) a = a + a + 11 (This is incorrect; it incorrectly suggests adding the term to itself before adding 11.) The correct recursive formula is not explicitly listed in the choices, but it is closest to choice (A) if we correct it to include the subscript n.

Which recursive formula can be used to define this sequence for n > 1? $\newline$ $1, 12, 23, 34, 45, 56, \ldots$ $\newline$ Choices: $\newline$ (A) $a_n = a_{n-1} + 11$ $\newline$ (B) $a_n = a_{n-1} - 11$ $\newline$ (C) $a_n = \frac{17}{6}a_{n-1}$ $\newline$ (D) $a_n = a_{n-1} + a_{n-1} + 11$

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