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# The sequence S is defined by Sn = 2(Sn – 1) – 4 for each integer n ≥ 2

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Joined: 02 Sep 2009
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The sequence S is defined by Sn = 2(Sn – 1) – 4 for each integer n ≥ 2  [#permalink]

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27 Jul 2018, 01:19
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Difficulty:

15% (low)

Question Stats:

90% (01:12) correct 10% (00:42) wrong based on 29 sessions

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The sequence S is defined by $$S_n = 2(S_{n – 1}) – 4$$ for each integer n ≥ 2. If $$S_1 = 6$$, what is the value of $$S_5$$?

(A) –20
(B) 16
(C) 20
(D) 24
(E) 36

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Re: The sequence S is defined by Sn = 2(Sn – 1) – 4 for each integer n ≥ 2  [#permalink]

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27 Jul 2018, 02:29
$$S_n = 2(S_{n – 1}) – 4$$

$$S_2 = 2(S_{2 – 1}) – 4 = 2(S_{1}) – 4 = 2(6) - 4 = 8$$

$$S_3 = 2(S_{3 – 1}) – 4 = 2(S_{2}) – 4 = 2(8) - 4 = 12$$

$$S_4 = 2(S_{4 – 1}) – 4 = 2(S_{3}) – 4 = 2(12) - 4 = 20$$

$$S_5 = 2(S_{5 – 1}) – 4 = 2(S_{4}) – 4 = 2(20) - 4 = 36$$

Hence option E
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Re: The sequence S is defined by Sn = 2(Sn – 1) – 4 for each integer n ≥ 2  [#permalink]

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27 Jul 2018, 02:38
Sn = 2*(Sn–1)–4
S1 = 6, S5 = ?

Now,
S2 = 2*(S1) – 4 = 2*6 - 4 = 12 - 4 = 8
S3 = 2*(S2) – 4 = 2*8 - 4 = 16 - 4 = 12
S4 = 2*(S3) – 4 = 2*12 - 4 = 24 - 4 = 20
S5 = 2*(S4) – 4 = 2*20 - 4 = 40 - 4 = 36

Hence, E.
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Re: The sequence S is defined by Sn = 2(Sn – 1) – 4 for each integer n ≥ 2 &nbs [#permalink] 27 Jul 2018, 02:38
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