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The sequence S is defined by Sn = Sn – 1 + Sn – 2 + Sn – 3 – 5 for eac

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V
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The sequence S is defined by Sn = Sn – 1 + Sn – 2 + Sn – 3 – 5 for eac  [#permalink]

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New post 27 Jul 2018, 01:25
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The sequence S is defined by \(S_n = S_{n – 1} + S_{n – 2} + S_{n – 3} – 5\) for each integer n ≥ 4. If \(S_1 = 4\), \(S_2 = 0\), and \(S_4 = –4\), what is the value of \(S_6\)?

(A) –2
(B) –12
(C) –16
(D) –20
(E) –24

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Re: The sequence S is defined by Sn = Sn – 1 + Sn – 2 + Sn – 3 – 5 for eac  [#permalink]

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New post 27 Jul 2018, 01:50
Sn = Sn–1 + Sn–2 + Sn–3 – 5
S1=4, S2=0, and S4=–4

S4 = S3 + S2 + S1 - 5
-4 = S3 + 0 + 4 - 5
S3 = -3

S5 = S4 + S3 + S2 - 5
S5 = -4 + (-3 ) + 0 - 5 = -12

S6 = S5 + S4 + S3 - 5 = -12 + (-4) + (-3) - 5 = -24

Hence, E.
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The sequence S is defined by Sn = Sn – 1 + Sn – 2 + Sn – 3 – 5 for eac  [#permalink]

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New post 27 Jul 2018, 21:44
Bunuel wrote:
The sequence S is defined by \(S_n = S_{n – 1} + S_{n – 2} + S_{n – 3} – 5\) for each integer n ≥ 4. If \(S_1 = 4\), \(S_2 = 0\), and \(S_4 = –4\), what is the value of \(S_6\)?

(A) –2
(B) –12
(C) –16
(D) –20
(E) –24


Let's find S_3

S4=S3+S2+S1-5......Substitute values in the equation

Then S3=-3

S5=S4+S3+S2-5..........No need to get the value

S6=S5+S4+S3-5......Substitute S_{5} from above then

S6=2S4+S3+S2-10 = -8 - 6 +0 -10 =-24

Answer: E
The sequence S is defined by Sn = Sn – 1 + Sn – 2 + Sn – 3 – 5 for eac &nbs [#permalink] 27 Jul 2018, 21:44
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