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Sequence Problem

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by Bens4vcobra » Tue Jul 05, 2011 6:00 am
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 a1?

A) 4

B) 24/7

C) 2

D) 12/7

E) 6/7
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by Frankenstein » Tue Jul 05, 2011 6:10 am
Hi,
a2 = 2a1,
a5 = (2^4)a1 = 16a1
a5 - a2 =12
So, 16a1 - 2a1 = 12 => a1 = 6/7

Hence, E
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by Bens4vcobra » Tue Jul 05, 2011 10:03 am
Frankenstein wrote:Hi,
a2 = 2a1,
a5 = (2^4)a1 = 16a1
a5 - a2 =12
So, 16a1 - 2a1 = 12 => a1 = 6/7

Hence, E
Could you explain a5 = (2^4)a1 = 16a1 a little further? I'm not seeing where that is coming from.
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by Frankenstein » Tue Jul 05, 2011 10:06 am
Bens4vcobra wrote:
Frankenstein wrote:Hi,
a2 = 2a1,
a5 = (2^4)a1 = 16a1
a5 - a2 =12
So, 16a1 - 2a1 = 12 => a1 = 6/7

Hence, E
Could you explain a5 = (2^4)a1 = 16a1 a little further? I'm not seeing where that is coming from.
Hi,
each term after the first is equal to twice the previous term.
So, a2 = 2a1
a3 = 2a2 = 2(2a1) = 4a1
Similarly, a4 = 2a3 = 8a1
a5 = 2a4 = 16a1.
Cheers!

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by worldpeace93 » Tue Jul 05, 2011 10:23 am
since r5-r2=12
a1r(r^3-1)=12

r= 2
hence a1= 6/7

hence OA E
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by GMATGuruNY » Tue Jul 05, 2011 1:57 pm
Bens4vcobra 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 a1?

A) 4

B) 24/7

C) 2

D) 12/7

E) 6/7
We can plug in the answers, which represent the value of a1.

Answer choice C: a1 = 2.
Since each term is equal to twice the previous term:
a2 = 4, a3 = 8, a4 = 16, and a5 = 32.
a5-a2 = 32-4 = 28.
Too big: the difference is supposed to be 12, which is less than 1/2 of 28.
Thus, the correct answer must be less than 1/2 the value of answer choice C.
Thus, the correct answer must be less than 1.

The correct answer is E.

Answer choice E: a1 = 6/7.
a2 = 12/7, a3 = 24/7, a4 = 48/7, and a5 = 96/7.
a5-a2 = 96/7 - 12/7 = 84/7 = 12.
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by MBA.Aspirant » Tue Jul 05, 2011 7:01 pm
Bens4vcobra 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 a1?

A) 4

B) 24/7

C) 2

D) 12/7

E) 6/7
x, 2x, 4x,8x, 16x

16x-2x = 12

14x=12

x= 12/14 = 6/7
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by amit2k9 » Tue Jul 05, 2011 9:26 pm
a5-a2=12

2^4a1-2a1 = 12

a1= 6/7
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by edvhou812 » Tue Jul 05, 2011 10:49 pm
If each term is equal to twice the previous, we can make a list and find that a5 = 8a2. From there we can work the following equation:

8a2-a2=12
7a2=12
a2=12/7

Since a2 is twice as much as a1, we get a1=(12/7)/(2/1)=12/7*1/2 = 6/7

Answer: E
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