Which recursive sequence would produce the sequence 3,-19,91,dots ? a_(1)=3 and a_(n)=-6a_(n-1)-1 a_(1)=3 and a_(n)=-5a_(n-1)-4 a_(1)=3 and a_(n)=-a_(n-1)-6 a_(1)=3 and a_(n)=-4a_(n-1)-5

Question

Which recursive sequence would produce the sequence  3,-19,91,dots ?  a_(1)=3 and  a_(n)=-6a_(n-1)-1  a_(1)=3 and  a_(n)=-5a_(n-1)-4  a_(1)=3 and  a_(n)=-a_(n-1)-6  a_(1)=3 and  a_(n)=-4a_(n-1)-5

Bytelearn · Accepted Answer

Identify First Term: Identify the first term of the sequence. The first term given is a_(1) = 3.Calculate Second Term: Calculate the second term using each recursive formula and compare with the given second term (-19). Using the first formula: a_(n) = -6a_(n-1) - 1 a_(2) = -6a_(1) - 1 = -6*3 - 1 = -18 - 1 = -19Verify Second Term: Verify if the second term calculated in Step 2 matches the given second term. The calculated second term using the first formula is -19, which matches the given second term.Calculate Third Term: Calculate the third term using the first recursive formula to verify if it matches the given third term (91). a_(3) = -6a_(2) - 1 = -6*(-19) - 1 = 114 - 1 = 113Check Third Term: Check if the third term calculated in Step 4 matches the given third term. The calculated third term using the first formula is 113, which does not match the given third term (91).Test Second Formula: Since the first formula did not produce the correct third term, test the second formula. Using the second formula: a_(n) = -5a_(n-1) - 4 a_(2) = -5a_(1) - 4 = -5*3 - 4 = -15 - 4 = -19Verify Second Term: Verify if the second term calculated in Step 6 matches the given second term. The calculated second term using the second formula is -19, which matches the given second term.Calculate Third Term: Calculate the third term using the second recursive formula to verify if it matches the given third term (91). a_(3) = -5a_(2) - 4 = -5*(-19) - 4 = 95 - 4 = 91Check Third Term: Check if the third term calculated in Step 8 matches the given third term. The calculated third term using the second formula is 91, which matches the given third term.Final Conclusion: Since the second formula has produced the correct second and third terms, we conclude that this is the correct recursive formula for the sequence. The correct recursive sequence formula is a_(1) = 3 and a_(n) = -5a_(n-1) - 4.

Which recursive sequence would produce the sequence $3,-19,91, \ldots$ ? $\newline$ $a_{1}=3$ and $a_{n}=-6 a_{n-1}-1$ $\newline$ $a_{1}=3$ and $a_{n}=-5 a_{n-1}-4$ $\newline$ $a_{1}=3$ and $a_{n}=-a_{n-1}-6$ $\newline$ $a_{1}=3$ and $a_{n}=-4 a_{n-1}-5$

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