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# The sequence S is defined by Sn = Sn – 1 + Sn – 2 – 3 for each integer

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Math Expert
Joined: 02 Sep 2009
Posts: 47967
The sequence S is defined by Sn = Sn – 1 + Sn – 2 – 3 for each integer  [#permalink]

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27 Jul 2018, 01:21
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Difficulty:

25% (medium)

Question Stats:

88% (01:38) correct 12% (01:24) wrong based on 17 sessions

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The sequence S is defined by $$S_n = S_{n – 1} + S_{n – 2} – 3$$ for each integer n ≥ 3. If $$S_1 = 5$$ and $$S_2 = 0$$, what is the value of $$S_6$$?

(A) –6
(B) –5
(C) –3
(D) –1
(E) 1

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

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27 Jul 2018, 02:08
Bunuel wrote:
The sequence S is defined by $$S_n = S_{n – 1} + S_{n – 2} – 3$$ for each integer n ≥ 3. If $$S_1 = 5$$ and $$S_2 = 0$$, what is the value of $$S_6$$?

(A) –6
(B) –5
(C) –3
(D) –1
(E) 1

$$S_3=S_2+S_1-3=5+0-3=2........S_4=2+0-3=-1$$..
$$S_5=-1+2-3=-2.........S_6=-2-1-3=-6$$
A
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Re: The sequence S is defined by Sn = Sn – 1 + Sn – 2 – 3 for each integer  [#permalink]

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27 Jul 2018, 02:45
Sn = Sn–1 + Sn–2 – 3
S1 = 5 and S2 = 0
S6 = ?

Now,
S3 = S2 + S1 – 3 = 0 + 5 - 3 = 2

S4 = S3 + S2 – 3 = 2 + 0 - 3 = -1

S5 = S4 + S3 – 3 = -1 + 2 - 3 = -2

S6 = S5 + S4 – 3 = -2 - 1 - 3 = -6

Hence, A.
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Re: The sequence S is defined by Sn = Sn – 1 + Sn – 2 – 3 for each integer &nbs [#permalink] 27 Jul 2018, 02:45
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