In the sequence a1,a2,a3,…, an,an is determined for all values of n2

Question

In the sequence  a_1 ,  a_2 ,  a_3 , …,  a_n ,  a_n  is determined for all values of  n>2  by taking the average of all terms  a_1  through  a_{n-1} . If  a_1=1 , what is the value of  a_7 ?

(1)  a_2=19

(2)  a_3=10

chetan2u · Answer

ans D...
1) statement 1 tells us a2 as 19 and a1 is given as 1.. therefore a3=10, a4=a5=a6=a7=10.. sufficient
2) statement 2 tells us a3 as 10 and a1 as 1 so a2 can be found similarily a7 = 10 ..sufficient

TudorM · Answer

Hello Bunuel, I gave it a try:

CORRECT ANSWER D

(1) is sufficient as if we know a2 and a1 we can find a3 (a3=(a1+a2)/s), so on and so forth up to a7 = 10 as well
(2) is sufficient as we know a3 and a1 and therefore we can find a2 and aftewards all answers up to a7 and a7 itself, a7 =10

Therefore both affirmations are sufficient, CORRECT ANSWER D

vedavyas9 · Answer

Given a1 = 1

a3 = (a1 + a2)/2 as per the question

if i know either a2 or a3, i can find a7.

statement 1: 
a2 = 19 - suffcient

statement 2:
a3 = 10 - sufficient

hence D

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

D. The key to nearly all sequence problems is to begin listing out the first few terms to arrive at a pattern. In this problem, beginning with statement 1, take a look at the first two terms:

1, 19

That means that the third term is the average of the first two terms, and is therefore 10. Which you should see matches statement 2 exactly (more on that in a second). If the first three terms, now (given only statement 1) are:

1, 19, 10

Then the sum of three terms is 30, and the average is again 10. So the fourth term is 10, and now you have:

1, 19, 10, 10

And you should see that the pattern will repeat indefinitely (if every new term is 10 and the original average is 10, the average won't change). So the answer must be 10, and statement 1 is sufficient.

Given statement 2, the same answers will hold. If the first term is 1 and the third is 10, then the second has to be 19. And at this point all the data is the same as it was for statement 1, so you're done - the answer again is 10, so statement 2 is also sufficient.

JFromm · Answer

Its answer D

Note: For all sequence questions start listing them

Statement 1: 1, 19, now take average of 1+19/2 = 10, so a3= 10
 1,19,10, now take average of 1+19+10/3 = 10, so a4 = 10 --> so in the long-run a7 must be 10 --> sufficient

Statement 2: Same answers must hold if there is 1,x,10, then we can conclude that x is 19, since 10 is the average from all numbers a1 to an-1 --> sufficient

Time: 1:20 min

Clycos · Answer

Hello,

What do you guys think about the fact that Statement 1 contradicts the sequence? If we know that a(n) is calculated using the averages of all terms from a(1) to a(n-1), shouldn't a(2) = 1 given that the average of a(1)=1?

Thank you,
Chris

Bunuel · Answer

You are missing important part of the stem:

In the sequence a1, a2, a3, …, an, an is determined  for all values of  n>2   by taking the average of all terms  a_1  through  a_{n-1} . If  a_1=1 , what is the value of  a_7 ?

So, this rule starts from  a_3 , which equals to the average of  a_1  and  a_2 .  a_4  equals to the average of  a_1 ,  a_2  and  a_3 , and so on.

bumpbot · Answer

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In the sequence a1,a2,a3,…, an,an is determined for all values of n>2

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