Which recursive sequence would produce the sequence 4,-22,108,dots ? a_(1)=4 and a_(n)=2a_(n-1)-6 a_(1)=4 and a_(n)=-2a_(n-1)-5 a_(1)=4 and a_(n)=-6a_(n-1)+2 a_(1)=4 and a_(n)=-5a_(n-1)-2

Question

Which recursive sequence would produce the sequence  4,-22,108,dots ?  a_(1)=4 and  a_(n)=2a_(n-1)-6  a_(1)=4 and  a_(n)=-2a_(n-1)-5  a_(1)=4 and  a_(n)=-6a_(n-1)+2  a_(1)=4 and  a_(n)=-5a_(n-1)-2

Bytelearn · Accepted Answer

Test Recursive Sequence 1: Let's test each recursive sequence by applying the given formulas to the initial term a_(1)=4 and see which one produces the sequence 4, -22, 108, ....  First, we'll test the recursive sequence a_(1)=4 and a_(n)=2a_(n-1)-6. a_(2) = 2a_(1) - 6 = 2*4 - 6 = 8 - 6 = 2 This does not match the second term of the sequence, which is -22.Test Recursive Sequence 2: Now, let's test the recursive sequence a_(1)=4 and a_(n)=-2a_(n-1)-5. a_(2) = -2a_(1) - 5 = -2*4 - 5 = -8 - 5 = -13 This does not match the second term of the sequence, which is -22.Test Recursive Sequence 3: Next, we'll test the recursive sequence a_(1)=4 and a_(n)=-6a_(n-1)+2. a_(2) = -6a_(1) + 2 = -6*4 + 2 = -24 + 2 = -22 This matches the second term of the sequence. Let's find the third term to see if the pattern continues. a_(3) = -6a_(2) + 2 = -6*(-22) + 2 = 132 + 2 = 134 This does not match the third term of the sequence, which is 108.Test Recursive Sequence 4: Finally, let's test the recursive sequence a_(1)=4 and a_(n)=-5a_(n-1)-2. a_(2) = -5a_(1) - 2 = -5*4 - 2 = -20 - 2 = -22 This matches the second term of the sequence. Let's find the third term to see if the pattern continues. a_(3) = -5a_(2) - 2 = -5*(-22) - 2 = 110 - 2 = 108 This matches the third term of the sequence. Therefore, this recursive sequence produces the given sequence.

Which recursive sequence would produce the sequence $4,-22,108, \ldots$ ? $\newline$ $a_{1}=4$ and $a_{n}=2 a_{n-1}-6$ $\newline$ $a_{1}=4$ and $a_{n}=-2 a_{n-1}-5$ $\newline$ $a_{1}=4$ and $a_{n}=-6 a_{n-1}+2$ $\newline$ $a_{1}=4$ and $a_{n}=-5 a_{n-1}-2$

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