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655-705 (Hard)|   Sequences|      
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Bunuel
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A sequence is defined by an+2 = an+1 an for n 1. If a1 = 3 and a2 01 Nov 2023, 00:59
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60% (02:29) correct 40% (02:57) wrong based on 141 sessions

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A sequence is defined by \(a_{n} = a_{n-1} − a_{n-2}\) for \(n ≥ 3\). If \(a_1 = 3\) and \(a_2 = 5\), what is the value of \(a_{2014}\)?

(A) −5
(B) −3
(C) 2
(D) 3
(E) 5
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varad98
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A sequence is defined by an+2 = an+1 an for n 1. If a1 = 3 and a2 03 Nov 2023, 01:25
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Bunuel
A sequence is defined by \(a_{n+2} = a_{n+1} − a_n\) for \(n ≥ 3\). If \(a_1 = 3\) and \(a_2 = 5\), what is the value of \(a_{2014}\)?

(A) −5
(B) −3
(C) 2
(D) 3
(E) 5
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Using provided formula. we get
a1=3
a2=5
a3=2
a4=-3
a5=-5
a6=-2
a7=3=a1

The sequence is made of 6 terms.
Hence divide 2014/6
Remainder= 4
Hence Selecting the 4th Term=-3

Hope this is correct.
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RiyazAhamed
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A sequence is defined by an+2 = an+1 an for n 1. If a1 = 3 and a2 13 Nov 2023, 03:51
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varad98
Bunuel
A sequence is defined by \(a_{n+2} = a_{n+1} − a_n\) for \(n ≥ 3\). If \(a_1 = 3\) and \(a_2 = 5\), what is the value of \(a_{2014}\)?

(A) −5
(B) −3
(C) 2
(D) 3
(E) 5

Using provided formula. we get
a1=3
a2=5
a3=2
a4=-3
a5=-5
a6=-2
a7=3=a1

The sequence is made of 6 terms.
Hence divide 2014/6
Remainder= 4
Hence Selecting the 4th Term=-3

Hope this is correct.
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How did you get the term 3? When we substitute 3 for n, we get a5 = a4 - a3. Is there a typo (instead of negative, I think it is given positive) in the given sequence?
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samarpan.g28
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A sequence is defined by an+2 = an+1 an for n 1. If a1 = 3 and a2 21 Dec 2023, 23:58
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varad98
Bunuel
A sequence is defined by \(a_{n+2} = a_{n+1} − a_n\) for \(n ≥ 3\). If \(a_1 = 3\) and \(a_2 = 5\), what is the value of \(a_{2014}\)?

(A) −5
(B) −3
(C) 2
(D) 3
(E) 5

Using provided formula. we get
a1=3
a2=5
a3=2
a4=-3
a5=-5
a6=-2
a7=3=a1

The sequence is made of 6 terms.
Hence divide 2014/6
Remainder= 4
Hence Selecting the 4th Term=-3

Hope this is correct.
Show more

I understood the solution, however, if n>=3 is already mentioned, how can we take n=1 to find the value of a3? Please help.
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Bunuel
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A sequence is defined by an+2 = an+1 an for n 1. If a1 = 3 and a2 22 Dec 2023, 00:06
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samarpan.g28
varad98
Bunuel
A sequence is defined by \(a_{n+2} = a_{n+1} − a_n\) for \(n ≥ 3\). If \(a_1 = 3\) and \(a_2 = 5\), what is the value of \(a_{2014}\)?

(A) −5
(B) −3
(C) 2
(D) 3
(E) 5

Using provided formula. we get
a1=3
a2=5
a3=2
a4=-3
a5=-5
a6=-2
a7=3=a1

The sequence is made of 6 terms.
Hence divide 2014/6
Remainder= 4
Hence Selecting the 4th Term=-3

Hope this is correct.

I understood the solution, however, if n>=3 is already mentioned, how can we take n=1 to find the value of a3? Please help.
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Yes, it would have been better if it were \(a_{n} = a_{n-1} − a_{n-2}\) instead. Fixed. Thank you!
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A sequence is defined by an+2 = an+1 an for n 1. If a1 = 3 and a2 06 Jan 2025, 02:15
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