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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 B. 24/7 C. 2 D. 12/7 E. 6/7
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Re: various questions [#permalink]
 21 Apr 2010, 07:37
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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.24/7 C.2 D.12/7 E.6/7
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Re: Algebra Sequence [#permalink]
16 Feb 2011, 06:09
This is clearly a geometric progression. The nth term of a GP is given by a1 r^(n-1) where r is the ratio between two successive terms a5 = a1 2^(5-1) = a1 2^4 = 16a1 a2 = a1 2^(2-1) = a1 2^1 = 2a1 a5 - a2 = 12 16a1 - 2a1 = 12 14a1 = 12 a1 = 12/14 a1 = 6/7
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Re: Algebra Sequence [#permalink]
16 Feb 2011, 06:32
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Re: Algebra Sequence [#permalink]
17 Feb 2011, 06:49
Baten80 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.24/7
C.2
D.12/7
E.6/7 Let the a1= xtherefore, a2=2x, a3=4x, a4=8x, a5=16x.It is given that a5-a2=12, that means: 16x-2x=12; 14x=12, therefore x=\frac{6}{7}= a1.Answer is E.
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Re: Algebra Sequence
[#permalink]
17 Feb 2011, 06:49
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