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

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18 Jun 2012, 01:24

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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 \(a_1\)?

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

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

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

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, \(a_1 = 12/14 = 6/7\)

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

----------------- +KUDOS is the way to say THANKS

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.

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

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10 Mar 2015, 04:15

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

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09 May 2016, 09:55

Hello from the GMAT Club BumpBot!

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