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16 Sep 2014, 01:18
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
87% (02:00) correct
13%
(02:04)
wrong
based on 119
sessions
History
Date
Time
Result
Not Attempted Yet
The sequence \(a_1\), \(a_2\), \(a_3\), ... , \(a_n\), ... is such that \(a_n=a_{n-1}+a_{n-2}\) for all \(n \ge 3\). If \(a_1 = 3\) and \(a_5 = 6\), what is the value of \(a_2\) ?
A. -3
B. -1
C. 0
D. 2
E. 3
A. -3
B. -1
C. 0
D. 2
E. 3
16 Sep 2014, 01:18
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Official Solution:
The sequence \(a_1\), \(a_2\), \(a_3\), ... , \(a_n\), ... is such that \(a_n=a_{n-1}+a_{n-2}\) for all \(n \ge 3\). If \(a_1 = 3\) and \(a_5 = 6\), what is the value of \(a_2\) ?
A. -3
B. -1
C. 0
D. 2
E. 3
Given that \(a_n=a_{n-1}+a_{n-2}\), we have:
\(a_5=\)
\(=a_4+a_3=\)
\(=(a_3+a_2)+(a_2+a_1)=\)
\(=((a_2+a_1)+a_2)+(a_2+a_1)=\)
\(=3*a_2+2*a_1\).
Thus, \(a_5=3*a_2+2*a_1\) or \(6=3*a_2+2*3\), which gives \(a_2=0\).
Answer: C
The sequence \(a_1\), \(a_2\), \(a_3\), ... , \(a_n\), ... is such that \(a_n=a_{n-1}+a_{n-2}\) for all \(n \ge 3\). If \(a_1 = 3\) and \(a_5 = 6\), what is the value of \(a_2\) ?
A. -3
B. -1
C. 0
D. 2
E. 3
Given that \(a_n=a_{n-1}+a_{n-2}\), we have:
\(a_5=\)
\(=a_4+a_3=\)
\(=(a_3+a_2)+(a_2+a_1)=\)
\(=((a_2+a_1)+a_2)+(a_2+a_1)=\)
\(=3*a_2+2*a_1\).
Thus, \(a_5=3*a_2+2*a_1\) or \(6=3*a_2+2*3\), which gives \(a_2=0\).
Answer: C
14 Mar 2018, 14:56
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I believe the best way to solve this question is using "TEST THE ANSWERS" or "BACKSOLVING".
Let's use "C" because zero is an easy number to work with.
An= An-1 + An-2
Where A1=3 and A5=6
If A2 = 0
A3= A2 + A1
A3= 0 + 3
A3 = 3
A4= A3 + A2
A4 = 3 + 0
A4 = 3
A5= A4 + A3
A5= 3 + 3
A5=6 That's a match
I hope it helps!!
Thanks! Ale
Let's use "C" because zero is an easy number to work with.
An= An-1 + An-2
Where A1=3 and A5=6
If A2 = 0
A3= A2 + A1
A3= 0 + 3
A3 = 3
A4= A3 + A2
A4 = 3 + 0
A4 = 3
A5= A4 + A3
A5= 3 + 3
A5=6 That's a match
I hope it helps!!
Thanks! Ale
