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

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

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.

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

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

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.

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