Which recursive sequence would produce the sequence 7,33,163,dots ? a_(1)=7 and a_(n)=5a_(n-1)-2 a_(1)=7 and a_(n)=5a_(n-1)+4 a_(1)=7 and a_(n)=4a_(n-1)+5 a_(1)=7 and a_(n)=-2a_(n-1)+5

Question

Which recursive sequence would produce the sequence  7,33,163,dots ?  a_(1)=7 and  a_(n)=5a_(n-1)-2  a_(1)=7 and  a_(n)=5a_(n-1)+4  a_(1)=7 and  a_(n)=4a_(n-1)+5  a_(1)=7 and  a_(n)=-2a_(n-1)+5

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Identify First Term: Identify the first term of the sequence. The first term given is a_(1) = 7.Find Second Term: Use the first recursive formula to find the second term. The first option is a_(n) = 5a_(n-1) - 2. Let's apply it to find a_(2). a_(2) = 5 * a_(1) - 2 = 5 * 7 - 2 = 35 - 2 = 33. This matches the second term of the sequence.Find Third Term: Use the first recursive formula to find the third term. Now, let's find a_(3) using the same formula. a_(3) = 5 * a_(2) - 2 = 5 * 33 - 2 = 165 - 2 = 163. This matches the third term of the sequence.Verify Other Options: Verify that the other options do not match the sequence. To ensure we have the correct formula, we should check that the other options do not produce the sequence. For the second option, a_(n) = 5a_(n-1) + 4, let's find a_(2). a_(2) = 5 * a_(1) + 4 = 5 * 7 + 4 = 35 + 4 = 39. This does not match the second term of the sequence.Check Second Option: Check the third option. For the third option, a_(n) = 4a_(n-1) + 5, let's find a_(2). a_(2) = 4 * a_(1) + 5 = 4 * 7 + 5 = 28 + 5 = 33. This matches the second term of the sequence, so we need to check the third term.Check Third Option: Find the third term using the third option. a_(3) = 4 * a_(2) + 5 = 4 * 33 + 5 = 132 + 5 = 137. This does not match the third term of the sequence.Check Fourth Option: Check the fourth option. For the fourth option, a_(n) = -2a_(n-1) + 5, let's find a_(2). a_(2) = -2 * a_(1) + 5 = -2 * 7 + 5 = -14 + 5 = -9. This does not match the second term of the sequence.Conclude Correct Formula: Conclude the correct recursive formula. Since only the first option produces the correct second and third terms of the sequence, we can conclude that the correct recursive formula is: a_(1) = 7 and a_(n) = 5a_(n-1) - 2.

Which recursive sequence would produce the sequence $7,33,163, \ldots$ ? $\newline$ $a_{1}=7$ and $a_{n}=5 a_{n-1}-2$ $\newline$ $a_{1}=7$ and $a_{n}=5 a_{n-1}+4$ $\newline$ $a_{1}=7$ and $a_{n}=4 a_{n-1}+5$ $\newline$ $a_{1}=7$ and $a_{n}=-2 a_{n-1}+5$

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