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# If the infinite sequence a1, a2, a3, ..., an, ..., each term

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If the infinite sequence a1, a2, a3, ..., an, ..., each term  [#permalink]

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Updated on: 18 Jun 2012, 01:31
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In the infinite sequence $$a_1$$, $$a_2$$, $$a_3$$,...., $$a_n$$, each term after the first is equal to twice the previous term. If $$a_5-a_2=12$$, what is the value of $$a_1$$?

A. 4
C. 2
D. 12/7
E. 6/7

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Originally posted by Stiv on 18 Jun 2012, 01:24.
Last edited by Bunuel on 18 Jun 2012, 01:31, edited 2 times in total.
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Re: If the infinite sequence a1, a2, a3, ..., an, ..., each term  [#permalink]

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18 Jun 2012, 01:30
In the infinite sequence $$a_1$$, $$a_2$$, $$a_3$$,...., $$a_n$$, each term after the first is equal to twice the previous term. If $$a_5-a_2=12$$, what is the value of $$a_1$$?

A. 4
C. 2
D. 12/7
E. 6/7

The formula for calculating $$n_{th}$$ term would be $$a_n=2^{n-1}*a_1$$ . So:
$$a_5=2^4*a_1$$;
$$a_2=2*a_1$$;

Given: $$a_5-a_2=2^4*a_1-2*a_1=12$$ --> $$2^4*a_1-2*a_1=12$$ --> $$a_1=\frac{12}{14}=\frac{6}{7}$$.

Hope it's clear.
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Re: If the infinite sequence a1, a2, a3, ..., an, ..., each term  [#permalink]

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18 Jun 2012, 02:50
2
Stiv wrote:
In the infinite sequence $$a_1$$, $$a_2$$, $$a_3$$,...., $$a_n$$, each term after the first is equal to twice the previous term. If $$a_5-a_2=12$$, what is the value of $$a_1$$?

A. 4
C. 2
D. 12/7
E. 6/7

First step for sequence questions is writing down the first few terms.
$$a_2 = 2*a_1$$
$$a_3 = 2*a_2 = 2*2*a_1$$
and so on..
$$a_5 - a_2 = 2*2*2*2*a_1 - 2*a_1 = 14 * a_1 = 12$$
So, $$a_1 = 12/14 = 6/7$$

For more on sequences, check out: http://www.veritasprep.com/blog/2012/03 ... sequences/
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Re: If the infinite sequence a1, a2, a3, ..., an, ..., each term  [#permalink]

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18 Jun 2012, 02:56
a1 = x
a2 = 2x
a3 = 4x
a4 = 16x
an = 2^(n-1)*x

a5-a2 = 2^4*x - 2x = 12
x(2^4 - 2) = 12
x(16 - 2) = 12
x = 12 / 14 = 6 / 7

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Re: If the infinite sequence a1, a2, a3, ..., an, ..., each term  [#permalink]

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18 Jun 2012, 05:30
Took me 2.5 minutes to solve this easy q. I was confused between substituting the answer and trying algebra
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Re: In the infinite sequence a1, a2,  [#permalink]

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19 Nov 2013, 03:40
1
amgelcer wrote:
In the infinite sequence a1, a2, a3, ..., an, ..., each term after the first is equal to twice the previous term. If a5 - a2, = 12, what is the value of a1?

(A)
4

(B)

(C)
2

(D)
12/7

(E)
6/7

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It is a Geometric Progression, with the common ratio as 2.

Thus, as $$t_n = a*r^{n-1}$$ , where a is the first term and r is the common ratio.

$$a_5 = a_1*2^4$$and $$a_2 = a_1*2^1$$

Thus,$$a_5-a_2 = a_1*14 = 12 \to a_1 = \frac{6}{7}$$

E.
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Re: If the infinite sequence a1, a2, a3, ..., an, ..., each term  [#permalink]

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09 May 2016, 10:10
Say a1= x

Then a5= 16x and a2= 2x

16x-2x= 12

x= 12/14= 6/7
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Re: If the infinite sequence a1, a2, a3, ..., an, ..., each term  [#permalink]

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20 Mar 2018, 06:23
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Re: If the infinite sequence a1, a2, a3, ..., an, ..., each term &nbs [#permalink] 20 Mar 2018, 06:23
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