Which recursive sequence would produce the sequence 9,-14,9,dots? a_(1)=9 and a_(n)=-a_(n-1)-5 a_(1)=9 and a_(n)=-5a_(n-1)-1 a_(1)=9 and a_(n)=4a_(n-1)-2 a_(1)=9 and a_(n)=-2a_(n-1)+4

Question

Which recursive sequence would produce the sequence  9,-14,9,dots?  a_(1)=9 and  a_(n)=-a_(n-1)-5  a_(1)=9 and  a_(n)=-5a_(n-1)-1  a_(1)=9 and  a_(n)=4a_(n-1)-2  a_(1)=9 and  a_(n)=-2a_(n-1)+4

Bytelearn · Accepted Answer

Test Recursive Formula 1: Let's test each given recursive formula by applying it to the initial term a_1 = 9 to see if it produces the sequence 9, -14, 9, ....  First, we'll test the recursive formula a_(n) = -a_(n-1) - 5 with a_1 = 9.  a_2 = -a_1 - 5 = -9 - 5 = -14 a_3 = -a_2 - 5 = -(-14) - 5 = 14 - 5 = 9  This matches the given sequence 9, -14, 9, ....Test Recursive Formula 2: Now let's test the second recursive formula a_(n) = -5a_(n-1) - 1 with a_1 = 9.  a_2 = -5a_1 - 1 = -5*9 - 1 = -45 - 1 = -46 This does not match the second term of the given sequence (-14), so this recursive formula is incorrect.Test Recursive Formula 3: Next, we'll test the third recursive formula a_(n) = 4a_(n-1) - 2 with a_1 = 9.  a_2 = 4a_1 - 2 = 4*9 - 2 = 36 - 2 = 34 This does not match the second term of the given sequence (-14), so this recursive formula is incorrect.Test Recursive Formula 4: Finally, let's test the fourth recursive formula a_(n) = -2a_(n-1) + 4 with a_1 = 9.  a_2 = -2a_1 + 4 = -2*9 + 4 = -18 + 4 = -14 a_3 = -2a_2 + 4 = -2*(-14) + 4 = 28 + 4 = 32 This does not match the third term of the given sequence (9), so this recursive formula is incorrect.

Which recursive sequence would produce the sequence $9,-14,9, \ldots ?$ $\newline$ $a_{1}=9$ and $a_{n}=-a_{n-1}-5$ $\newline$ $a_{1}=9$ and $a_{n}=-5 a_{n-1}-1$ $\newline$ $a_{1}=9$ and $a_{n}=4 a_{n-1}-2$ $\newline$ $a_{1}=9$ and $a_{n}=-2 a_{n-1}+4$

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