Which recursive sequence would produce the sequence 7,-33,167,dots ? a_(1)=7 and a_(n)=2a_(n-1)-5 a_(1)=7 and a_(n)=-5a_(n-1)+2 a_(1)=7 and a_(n)=-4a_(n-1)-5 a_(1)=7 and a_(n)=-5a_(n-1)-4

Question

Which recursive sequence would produce the sequence  7,-33,167,dots ?  a_(1)=7 and  a_(n)=2a_(n-1)-5  a_(1)=7 and  a_(n)=-5a_(n-1)+2  a_(1)=7 and  a_(n)=-4a_(n-1)-5  a_(1)=7 and  a_(n)=-5a_(n-1)-4

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Identify First Term: Identify the first term of the sequence. The first term given is a_(1) = 7.Test First Formula: Use the second term to test the recursive formulas. The second term in the sequence is -33. We will substitute n = 2 into each recursive formula to see which one yields -33 when the first term is 7.  For the first formula: a_(2) = 2a_(1) - 5 a_(2) = 2(7) - 5 a_(2) = 14 - 5 a_(2) = 9 This does not match the second term of the sequence, which is -33.Test Second Formula: Test the second recursive formula. For the second formula: a_(2) = -5a_(1) + 2 a_(2) = -5(7) + 2 a_(2) = -35 + 2 a_(2) = -33 This matches the second term of the sequence.Verify Third Term: Verify the third term using the correct formula from Step 3. The third term in the sequence is 167. We will now check if this term can be obtained by applying the recursive formula a_(n) = -5a_(n-1) + 2 with n = 3.  a_(3) = -5a_(2) + 2 a_(3) = -5(-33) + 2 a_(3) = 165 + 2 a_(3) = 167 This matches the third term of the sequence.Conclude Correct Formula: Conclude that the correct recursive formula is found. Since the recursive formula a_(n) = -5a_(n-1) + 2 produces the correct second and third terms of the sequence when starting with a_(1) = 7, we can conclude that this is the correct recursive formula for the given sequence.

Which recursive sequence would produce the sequence $7,-33,167, \ldots$ ? $\newline$ $a_{1}=7$ and $a_{n}=2 a_{n-1}-5$ $\newline$ $a_{1}=7$ and $a_{n}=-5 a_{n-1}+2$ $\newline$ $a_{1}=7$ and $a_{n}=-4 a_{n-1}-5$ $\newline$ $a_{1}=7$ and $a_{n}=-5 a_{n-1}-4$

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