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# Each number SN in a sequence can be expressed as a function of the pre

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Math Expert
Joined: 02 Sep 2009
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Each number SN in a sequence can be expressed as a function of the pre  [#permalink]

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09 Jul 2018, 04:57
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Difficulty:

45% (medium)

Question Stats:

63% (03:02) correct 37% (02:29) wrong based on 35 sessions

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Each number $$S_n$$ in a sequence can be expressed as a function of the preceding number ($$S_{n–1}$$) as follows: $$S_n = \frac{2}{3}*S_{n–1} – 4$$. Which of the following equations correctly expresses the value of SN in this sequence in terms of SN+2?

A) $$S_n = \frac{9}{4}*S_{n+2} +18$$

B) $$S_n = \frac{4}{9} *S_{n+2} +15$$

C) $$S_n = \frac{9}{4}*S_{n+2} + 15$$

D) $$S_n = \frac{4}{9}*S_{n+2} - 8$$

E) $$S_n = \frac{2}{3}*S_{n+2} -8$$

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Re: Each number SN in a sequence can be expressed as a function of the pre  [#permalink]

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09 Jul 2018, 06:08
$$S_n = \frac{2}{3}*S_{n–1} – 4$$

$$S_{n+2} = \frac{2}{3}*S_{n+1} – 4$$ --- (1)

$$S_{n+1} = \frac{2}{3}*S_{n} – 4$$ --- (2)

Substitute (2) in (1) --> $$S_{n+2} = \frac{4}{9}*S_{n} – \frac{8}{3} - 4$$

$$S_{n+2} = \frac{4}{9}*S_{n} – \frac{60}{9}$$

$$9S_{n+2} = 4*S_{n} – 60$$

$$S_{n} = \frac{9}{4}*S_{n+2} + 15$$

Bunuel wrote:
Each number $$S_n$$ in a sequence can be expressed as a function of the preceding number ($$S_{n–1}$$) as follows: $$S_n = \frac{2}{3}*S_{n–1} – 4$$. Which of the following equations correctly expresses the value of SN in this sequence in terms of SN+2?

A) $$S_n = \frac{9}{4}*S_{n+2} +18$$

B) $$S_n = \frac{4}{9} *S_{n+2} +15$$

C) $$S_n = \frac{9}{4}*S_{n+2} + 15$$

D) $$S_n = \frac{4}{9}*S_{n+2} - 8$$

E) $$S_n = \frac{2}{3}*S_{n+2} -8$$
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Re: Each number SN in a sequence can be expressed as a function of the pre  [#permalink]

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09 Jul 2018, 06:13
Bunuel wrote:
Each number $$S_n$$ in a sequence can be expressed as a function of the preceding number ($$S_{n–1}$$) as follows: $$S_n = \frac{2}{3}*S_{n–1} – 4$$. Which of the following equations correctly expresses the value of SN in this sequence in terms of SN+2?

A) $$S_n = \frac{9}{4}*S_{n+2} +18$$

B) $$S_n = \frac{4}{9} *S_{n+2} +15$$

C) $$S_n = \frac{9}{4}*S_{n+2} + 15$$

D) $$S_n = \frac{4}{9}*S_{n+2} - 8$$

E) $$S_n = \frac{2}{3}*S_{n+2} -8$$

$$S_{n+2}=\frac{2}{3}S_{n+2-1}-4$$=$$\frac{2}{3} (S_{n+1}-4)$$=$$\frac{2}{3}(\frac{2}{3}S_{n+1-1}-4)-4$$=$$\frac{4}{9}S_{n}-\frac{8}{3}$$-4=$$\frac{4}{9}s_{n}-\frac{20}{3}$$
Or,$$\frac{4}{9}S_{n}=S_{n+2}+\frac{20}{3}$$
Or, $$S_n = \frac{9}{4}*S_{n+2} + 15$$ (multiplying both sides by $$\frac{9}{4}$$)
Ans. (C)
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Re: Each number SN in a sequence can be expressed as a function of the pre &nbs [#permalink] 09 Jul 2018, 06:13
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