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02 Aug 2023, 12:00
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A
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In the sequence \(a_1, \ a_2, \ a_3, \ ..., \ a_n, \ ...\), the terms \(a_i\), \(a_{i+1}\), and \(a_{i+2}\) satisfy the equation \(a_{i+2} = 2a_{i+1} + 3a_i\) for all positive integers i. If \(a_3 = 9\) and \(a_5 = 51\), what is the value of \(a_4\)?
A. 12
B. 30
C. 72
D. 129
E. 171
A. 12
B. 30
C. 72
D. 129
E. 171
02 Aug 2023, 21:27
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Bunuel
In the sequence \(a_1, \ a_2, \ a_3, \ ..., \ a_n, \ ...\), the terms \(a_i\), \(a_i+1\), and \(a_i+2\) satisfy the equation \(a_{i+2} = 2a_{i+1} + 3a_i\) for all positive integers i. If \(a_3 = 9\) and \(a_5 = 51\), what is the value of \(a_4\)?
A. 12
B. 30
C. 72
D. 129
E. 171
A. 12
B. 30
C. 72
D. 129
E. 171
\(a_{i+2} = 2a_{i+1} + 3a_i\)
For i = 3
\(a_{5} = 2a_{4} + 3a_3\)
\(51 = 2a_{4} + (3*9)\)
\(2a_{4} = 51 - 27\)
\(a_{4} = 12\)
Option A
General Discussion
06 Aug 2023, 15:14
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Bunuel
In the sequence \(a_1, \ a_2, \ a_3, \ ..., \ a_n, \ ...\), the terms \(a_i\), \(a_{i+1}\), and \(a_{i+2}\) satisfy the equation \(a_{i+2} = 2a_{i+1} + 3a_i\) for all positive integers i. If \(a_3 = 9\) and \(a_5 = 51\), what is the value of \(a_4\)?
A. 12
B. 30
C. 72
D. 129
E. 171
A. 12
B. 30
C. 72
D. 129
E. 171
If i = 3, then i + 1 = 4 and i + 2 = 5.
a₅ = 2a₄ + 3a₃
51 = 2a₄ + 3(9)
2a₄ = 24
a₄ = 12
Answer: A
