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Re: The sequence a1,a2,…,an,… is such that an=(an−1)(an−3) for [#permalink]

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28 Jan 2015, 09:23

1

This post received KUDOS

Is the answer C?

Below is my solution

a4 = sq(a3*a1) option 1 gives us a1 value.--(1) a6 = sq(a5*a3) and a5 =sq(a4*a2)..option 2 gives us a2 value..combining (1)+(2) gives a6 .. a2 value is given in option2 hence using

Re: The sequence a1,a2,…,an,… is such that an=(an−1)(an−3) for [#permalink]

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28 Jan 2015, 09:23

1

This post received KUDOS

Is the answer C?

Below is my solution

a4 = sq(a3*a1) option 1 gives us a1 value.--(1) a6 = sq(a5*a3) and a5 =sq(a4*a2)..option 2 gives us a2 value..combining (1)+(2) gives a6 .. a2 value is given in option2 hence using

Re: The sequence a1,a2,…,an,… is such that an=(an−1)(an−3) for [#permalink]

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28 Jan 2015, 14:52

1

This post received KUDOS

Bunuel wrote:

The sequence a1, a2, …, an, … is such that \(a_n=\sqrt{a_{n-1}*a_{n-3}}\) for all integers n≥4. If \(a_4=16\), what is the value of a6?

(1) a1=2 (2) a2=4

Kudos for a correct solution.

Answer is C:

from stem: a4 =16

from 1: a1 = 2, from stem a4 = sqrt(2*a3) ==> 16 = sqrt(2*a3), so a3 = 128, we just know the sequence as 2,a2,126,15,a5..., we need a5 to find a6, so NSF

from 2: a2 = 4, as a1 is not known, this statement itslef is insufficient NSF

combined 1+2: a5 = sqrt(a4*a2) = 8, sequence is like 2,4,128,16,8,..we have all values to find a6 so C

One key for this problem, which looks worse than it actually is, is to avoid actually solving for the values. We only need to answer the question of whether a certain value can be solved for, not the more difficult question of what value would actually result.

The sequence rule gives that \(a_6=\sqrt{(a_5)(a_3)}\). In order to obtain the value of a6, we will need to obtain the values of both a5 and a3. Standing alone, a4 cannot produce either.

Adding statement (1) to the mix, we have the values of a1 and a4. Using the sequence rule with n=4 gives \(a_4=\sqrt{(a_3)(a_1)}\). Since we have both a4 and a1, this equation will allow us to solve for a3. From there, however, we can go no further. The values of a1,a3, and a4 do not collectively produce any of the other terms, and, in particular, we cannot solve for a5 with this information. Statement (1) alone is insufficient.

Taking statement (2) alone, we have the values of a2 and a4. Using the sequence rule with n = 5 gives \(a_5=\sqrt{(a_4)(a_2)}\). We have both a4 and a2, so we can get a5. Again, though, we reach a dead end. The values of a2,a4, and a5 do not collectively produce any of the other terms, and, in particular, we cannot solve for a3 with this information. Statement (2) alone is insufficient.

Combining the two statements, we are able to obtain all values from a1 through a5 (and beyond). In particular, statement (1) allows us to solve for a3, and statement (2) allows us to solve for a5. Recalling that \(a_6=\sqrt{(a_5)(a_3)}\), we know that we will be able to obtain a6. The two statements taken together are sufficient.
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