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# In the sequence an = (x + (–1)n –1)(an–1) and a1 = 1, which of the

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Math Expert
Joined: 02 Sep 2009
Posts: 46305
In the sequence an = (x + (–1)n –1)(an–1) and a1 = 1, which of the [#permalink]

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07 Sep 2017, 23:19
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Difficulty:

25% (medium)

Question Stats:

82% (01:46) correct 18% (01:43) wrong based on 90 sessions

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In the sequence $$a_n = (x + (–1)^{(n –1)})(a_{n–1})$$ and $$a_1 = 1$$, which of the following expresses a4?

A. $$x^2 – 1$$

B. $$x^3 – x^2 – x + 1$$

C. $$x^3 + x^2 + x – 1$$

D. $$x^4 – 2x^2 + 1$$

E. $$x^4 + 2x^2 – 1$$

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Manager
Joined: 12 Feb 2017
Posts: 71
In the sequence an = (x + (–1)n –1)(an–1) and a1 = 1, which of the [#permalink]

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07 Sep 2017, 23:35
An=(x+(–1)^(n–1))(An–1)
let's simplify this sequence
An= x*(An-1) + (-1)^(n-1) * (An-1)
A1=1

A2= x*(1) + (-1)^(2-1) * (1)
=x+ (-1)^(1) *(1)
=x-1

A3= (x)*(x-1) + (-1)^(3-1) * (x-1)
= x^2 -x + (1)*(x-1)
=x^2 -x+x-1
=x^2 -1

A4 =x*(x^2 -1) + (-1)^(4-1) * (x^2 -1)
=x^3 -x + (-1)*(x^2 -1)
=x^3 - x^2 - x +1

Kudos if it helps.
Intern
Joined: 14 Oct 2016
Posts: 32
Location: India
WE: Sales (Energy and Utilities)
Re: In the sequence an = (x + (–1)n –1)(an–1) and a1 = 1, which of the [#permalink]

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08 Sep 2017, 13:44
{x+(–1)^(n–1)}
this term would be either (x-1) if n is even or (x+1) if n is odd

So
a(4)= (x-1) {(x+1)(x-1)}

Simplifying Gives us choice B
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Abhimanyu

Re: In the sequence an = (x + (–1)n –1)(an–1) and a1 = 1, which of the   [#permalink] 08 Sep 2017, 13:44
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