Which recursive sequence would produce the sequence 1,-5,13,dots ? a_(1)=1 and a_(n)=-a_(n-1)-4 a_(1)=1 and a_(n)=-2a_(n-1)-3 a_(1)=1 and a_(n)=-4a_(n-1)-1 a_(1)=1 and a_(n)=-3a_(n-1)-2

Question

Which recursive sequence would produce the sequence  1,-5,13,dots ?  a_(1)=1 and  a_(n)=-a_(n-1)-4  a_(1)=1 and  a_(n)=-2a_(n-1)-3  a_(1)=1 and  a_(n)=-4a_(n-1)-1  a_(1)=1 and  a_(n)=-3a_(n-1)-2

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Test Option 1: Let's test the first option: a_(1)=1 and a_(n)=-a_(n-1)-4. We start with a_(1)=1. To find a_(2), we use the recursive formula: a_(2)=-a_(1)-4 = -1-4 = -5. Now, let's find a_(3): a_(3)=-a_(2)-4 = -(-5)-4 = 5-4 = 1. This does not match the given sequence since the third term should be 13, not 1.Test Option 2: Let's test the second option: a_(1)=1 and a_(n)=-2a_(n-1)-3. We start with a_(1)=1. To find a_(2), we use the recursive formula: a_(2)=-2a_(1)-3 = -2*1-3 = -2-3 = -5. Now, let's find a_(3): a_(3)=-2a_(2)-3 = -2*(-5)-3 = 10-3 = 7. This does not match the given sequence since the third term should be 13, not 7.Test Option 3: Let's test the third option: a_(1)=1 and a_(n)=-4a_(n-1)-1. We start with a_(1)=1. To find a_(2), we use the recursive formula: a_(2)=-4a_(1)-1 = -4*1-1 = -4-1 = -5. Now, let's find a_(3): a_(3)=-4a_(2)-1 = -4*(-5)-1 = 20-1 = 19. This does not match the given sequence since the third term should be 13, not 19.Test Option 4: Let's test the fourth option: a_(1)=1 and a_(n)=-3a_(n-1)-2. We start with a_(1)=1. To find a_(2), we use the recursive formula: a_(2)=-3a_(1)-2 = -3*1-2 = -3-2 = -5. Now, let's find a_(3): a_(3)=-3a_(2)-2 = -3*(-5)-2 = 15-2 = 13. This matches the given sequence since the third term is indeed 13.

Which recursive sequence would produce the sequence $1,-5,13, \ldots$ ? $\newline$ $a_{1}=1$ and $a_{n}=-a_{n-1}-4$ $\newline$ $a_{1}=1$ and $a_{n}=-2 a_{n-1}-3$ $\newline$ $a_{1}=1$ and $a_{n}=-4 a_{n-1}-1$ $\newline$ $a_{1}=1$ and $a_{n}=-3 a_{n-1}-2$

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