Which recursive sequence would produce the sequence 2,8,26,dots ? a_(1)=2 and a_(n)=3a_(n-1)+2 a_(1)=2 and a_(n)=2a_(n-1)+3 a_(1)=2 and a_(n)=4a_(n-1)+2 a_(1)=2 and a_(n)=2a_(n-1)+4

Question

Which recursive sequence would produce the sequence  2,8,26,dots ?  a_(1)=2 and  a_(n)=3a_(n-1)+2  a_(1)=2 and  a_(n)=2a_(n-1)+3  a_(1)=2 and  a_(n)=4a_(n-1)+2  a_(1)=2 and  a_(n)=2a_(n-1)+4

Bytelearn · Accepted Answer

Identify First Term: Identify the first term of the sequence. The first term given is a_(1) = 2, which is the starting point for our recursive sequence.Calculate Second Term: Calculate the second term using each recursive formula and compare with the given second term of the sequence (8). Using the first formula: a_(n) = 3a_(n-1) + 2, the second term would be a_(2) = 3a_(1) + 2 = 3*2 + 2 = 8. Using the second formula: a_(n) = 2a_(n-1) + 3, the second term would be a_(2) = 2a_(1) + 3 = 2*2 + 3 = 7. Using the third formula: a_(n) = 4a_(n-1) + 2, the second term would be a_(2) = 4a_(1) + 2 = 4*2 + 2 = 10. Using the fourth formula: a_(n) = 2a_(n-1) + 4, the second term would be a_(2) = 2a_(1) + 4 = 2*2 + 4 = 8.Eliminate Incorrect Formulas: Eliminate the formulas that do not match the second term of the sequence. The second formula and the third formula do not match the given second term (8), so they can be eliminated.Calculate Third Term: Calculate the third term using the remaining recursive formulas and compare with the given third term of the sequence (26). Using the first formula: a_(3) = 3a_(2) + 2 = 3*8 + 2 = 24 + 2 = 26. Using the fourth formula: a_(3) = 2a_(2) + 4 = 2*8 + 4 = 16 + 4 = 20.Eliminate Incorrect Formula: Eliminate the formula that does not match the third term of the sequence. The fourth formula does not match the given third term (26), so it can be eliminated.Confirm Correct Formula: Confirm the correct recursive formula. The first formula matches both the second and third terms of the sequence, so it is the correct recursive formula.

Which recursive sequence would produce the sequence $2,8,26, \ldots$ ? $\newline$ $a_{1}=2$ and $a_{n}=3 a_{n-1}+2$ $\newline$ $a_{1}=2$ and $a_{n}=2 a_{n-1}+3$ $\newline$ $a_{1}=2$ and $a_{n}=4 a_{n-1}+2$ $\newline$ $a_{1}=2$ and $a_{n}=2 a_{n-1}+4$

Full solution

More problems from Identify a sequence as explicit or recursive

Related topics