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14 Jun 2012, 02:38
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
87% (01:49) correct
13%
(01:48)
wrong
based on 4074
sessions
History
Date
Time
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Not Attempted Yet
The sequence \(a_1\), \(a_2\), \(a_3\), ... , \(a_n\), ... is such that \(a_n=\frac{a_{n-1}+a_{n-2}}{2}\) for all \(n\geq{3}\). If \(a_3 = 4\) and \(a_5 = 20\), what is the value of \(a_6\) ?
(A) 12
(B) 16
(C) 20
(D) 24
(E) 28
(A) 12
(B) 16
(C) 20
(D) 24
(E) 28
14 Jun 2012, 02:39
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SOLUTION
The sequence \(a_1\), \(a_2\), \(a_3\), ... , \(a_n\), ... is such that \(a_n=\frac{a_{n-1}+a_{n-2}}{2}\) for all \(n\geq{3}\). If \(a_3 = 4\) and \(a_5 = 20\), what is the value of \(a_6\) ?
(A) 12
(B) 16
(C) 20
(D) 24
(E) 28
Since given that \(a_n=\frac{a_{n-1}+a_{n-2}}{2}\), then:
\(a_5=\frac{a_{4}+a_{3}}{2}\) --> \(20=\frac{a_{4}+4}{2}\) --> \(a_4=36\);
\(a_6=\frac{a_{5}+a_{4}}{2}\) --> \(a_6=\frac{20+36}{2}\) --> \(a_6=28\).
Answer: E.
The sequence \(a_1\), \(a_2\), \(a_3\), ... , \(a_n\), ... is such that \(a_n=\frac{a_{n-1}+a_{n-2}}{2}\) for all \(n\geq{3}\). If \(a_3 = 4\) and \(a_5 = 20\), what is the value of \(a_6\) ?
(A) 12
(B) 16
(C) 20
(D) 24
(E) 28
Since given that \(a_n=\frac{a_{n-1}+a_{n-2}}{2}\), then:
\(a_5=\frac{a_{4}+a_{3}}{2}\) --> \(20=\frac{a_{4}+4}{2}\) --> \(a_4=36\);
\(a_6=\frac{a_{5}+a_{4}}{2}\) --> \(a_6=\frac{20+36}{2}\) --> \(a_6=28\).
Answer: E.
14 Jun 2012, 05:58
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Hi,
This one has be solved step by step, and there is chance of making mistakes.
Difficulty level: 600
\(a_n=\frac{a_{n-1}+a_{n-2}}2\)
or a_n is the average of last two terms,
thus,
\(\frac{a_3+a_4}2=a_5\)
\(\frac{a_4+a_5}2=a_6\)
Subtracting these equations;
\(\frac{a_5-a_3}2=a_6-a_5\)
\(a_6=\frac{3a_5-a_3}2=\frac{3*20-4}2=28\)
Thus, Answer is (E).
Regards,
This one has be solved step by step, and there is chance of making mistakes.
Difficulty level: 600
\(a_n=\frac{a_{n-1}+a_{n-2}}2\)
or a_n is the average of last two terms,
thus,
\(\frac{a_3+a_4}2=a_5\)
\(\frac{a_4+a_5}2=a_6\)
Subtracting these equations;
\(\frac{a_5-a_3}2=a_6-a_5\)
\(a_6=\frac{3a_5-a_3}2=\frac{3*20-4}2=28\)
Thus, Answer is (E).
Regards,
