Which recursive sequence would produce the sequence 2,9,44,dots ? a_(1)=2 and a_(n)=6a_(n-1)-3 a_(1)=2 and a_(n)=5a_(n-1)-1 a_(1)=2 and a_(n)=-3a_(n-1)+6 a_(1)=2 and a_(n)=-a_(n-1)+5

Question

Which recursive sequence would produce the sequence  2,9,44,dots ?  a_(1)=2 and  a_(n)=6a_(n-1)-3  a_(1)=2 and  a_(n)=5a_(n-1)-1  a_(1)=2 and  a_(n)=-3a_(n-1)+6  a_(1)=2 and  a_(n)=-a_(n-1)+5

Bytelearn · Accepted Answer

Test First Option: We will test each recursive sequence option by applying the given formula to the initial term a_(1)=2 and checking if it produces the sequence 2, 9, 44, .... We start with the first option: a_(1)=2 and  a_(n)=6a_(n-1)-3Calculate Second Term: Calculate the second term using the first option's formula: a_(2)=6a_(1)-3 a_(2)=6*2-3 a_(2)=12-3 a_(2)=9 This matches the second term of the sequence.Calculate Third Term: Calculate the third term using the first option's formula: a_(3)=6a_(2)-3 a_(3)=6*9-3 a_(3)=54-3 a_(3)=51 This does not match the third term of the sequence (which is 44), so the first option is incorrect.Test Second Option: Now we test the second option: a_(1)=2 and  a_(n)=5a_(n-1)-1Calculate Second Term: Calculate the second term using the second option's formula: a_(2)=5a_(1)-1 a_(2)=5*2-1 a_(2)=10-1 a_(2)=9 This matches the second term of the sequence.Calculate Third Term: Calculate the third term using the second option's formula: a_(3)=5a_(2)-1 a_(3)=5*9-1 a_(3)=45-1 a_(3)=44 This matches the third term of the sequence, so the second option is correct.Correct Recursive Sequence: We do not need to test the remaining options because we have found the correct recursive sequence that produces the sequence 2, 9, 44, ....

Which recursive sequence would produce the sequence $2,9,44, \ldots$ ? $\newline$ $a_{1}=2$ and $a_{n}=6 a_{n-1}-3$ $\newline$ $a_{1}=2$ and $a_{n}=5 a_{n-1}-1$ $\newline$ $a_{1}=2$ and $a_{n}=-3 a_{n-1}+6$ $\newline$ $a_{1}=2$ and $a_{n}=-a_{n-1}+5$

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