The sequence a1,a2,,an, is such that an=(an1)(an3) for

Question

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

Pragnya87 · Answer

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

Pragnya87 · Answer

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

shriramvelamuri · Answer

IMO- Answer should be C. Please post OA.

santorasantu · Answer

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

buddyisraelgmat · Answer

To Find a6 , we need to know the values of a5 & a3

Stmnt 1 - gives value of a3 - Not Suff
Stmtn 2 - gives value of a5 - Not suff

Combined - Suff

Ans - C

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

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.

AbhimanyuDhar · Answer

Bunuel ,

Is this approach right.

√(ab)=√a√b ,

So a4= √a3*√a1
a5= √a4*√a2
a6= √a5*√a3
Weare given a4=16
a4= √a3*√a1

STMT 1: a1=2 .

16=√a3*√2

so √a3= 16/√2 = 8√2

STM2: a2=4

a5= √a4*√a2

a5=√16*√4

a5= 8

a6= √a5*√a3
 From above we can find the value of a6

Bambi2021 · Answer

Only by knowing that...

a1 = 2
a3 = 128
a4 = 16

...can't we solve this using some kind of pattern recognition? I mean, all values in a sequence are related. Or are there more than one equation (string of operations?) that could possibly lie behind this pattern?

WannaManaConsult · Answer

To get A6, we need A3 and A5. To get A5, we need A2 and A4.

1) A1=2
sqrt( 2 * A3) = 16
A3= 256
But this doesn't help us get A2, which means we can't get the A5 needed for A6.
Insufficient

2) A2 = 4
This helps us get A5, but A3 is still unaccounted for so we still can't get A6.
Insufficient.

1) helps us get A2, 2) helps us get A5, we have both of the numbers needed to get A6.

Answer: C

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

The sequence a1,a2,,an, is such that an=(an1)(an3) for

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

The sequence a1,a2,,an, is such that an=(an1)(an3) for

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards