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# The sequence S is defined by Sn = Sn – 1 + Sn – 2 – 1 for ea

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Joined: 07 Jun 2014
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GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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The sequence S is defined by Sn = Sn – 1 + Sn – 2 – 1 for ea [#permalink]  25 Jul 2018, 17:27
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Question Stats:

60% (00:57) correct 40% (00:49) wrong based on 5 sessions
The sequence S is defined by $$S_n = S_{n - 1} + S{n - 2} - 1$$ for each integer n ≥ 3. If $$S_1 = 11$$ and $$S_3 = 10$$, what is the value of $$S_5$$?

(A) 0
(B) 9
(C) 10
(D) 18
(E) 19
[Reveal] Spoiler: OA

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Sandy
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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1782 [0], given: 397

Re: The sequence S is defined by Sn = Sn – 1 + Sn – 2 – 1 for ea [#permalink]  11 Aug 2018, 17:00
Expert's post
Explanation

The sequence $$S_n = S_{n - 1} + S_{n - 2} - 1$$ can be read as “to get any term in sequence S, sum the two previous terms and subtract 1.”

The problem gives the first term and the third term and asks for the fifth term:

 11 10 $$S_1$$ $$S_2$$ $$S_3$$ $$S_4$$ $$S_5$$

Within the sequence $$S_1$$ to $$S_3$$, the problem gives two values but not the middle one ($$S_2$$). What version of the formula would include those three terms?

$$S_3 = S_2 + S_1 - 1$$

$$10 = S_2 + (11) - 1$$

$$10 = S_2 + 10$$

$$0 = S_2$$

 11 0 10 $$S_1$$ $$S_2$$ $$S_3$$ $$S_4$$ $$S_5$$

To get each subsequent term, sum the two previous terms and subtract 1. Thus, $$S_4 = 10 + 0 - 1 = 9$$ and $$S_5 = 9 + 10 - 1 = 18$$:

 11 0 10 9 18 $$S_1$$ $$S_2$$ $$S_3$$ $$S_4$$ $$S_5$$

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Sandy
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Re: The sequence S is defined by Sn = Sn – 1 + Sn – 2 – 1 for ea   [#permalink] 11 Aug 2018, 17:00
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