oquiella wrote:This is a sequence problem with a and n is right below it. Please repost with the right formatting if possible. I am not sure how to do it. See problem below.


In the sequence A1,A2, A3..., An, An is determined for all values of n>2 by taking the average of all terms A1 through An-1. If A1=1, what is the value of A7?

(1) A2=19
(2) A3=10


[/img]

DavidG@VeritasPrep wrote:

oquiella wrote:This is a sequence problem with a and n is right below it. Please repost with the right formatting if possible. I am not sure how to do it. See problem below.


In the sequence A1,A2, A3..., An, An is determined for all values of n>2 by taking the average of all terms A1 through An-1. If A1=1, what is the value of A7?

(1) A2=19
(2) A3=10


[/img]

Statement 1 tell us that A2=19. If each term (after the second term) is determined by taking the average of all terms A1 through An-1, then we know that A3 is the average of the first two terms, or (1+19)/2 = 10. Similarly, we know that A4 is the average of the first three terms, or (1 + 19 + 10)/3 = 10, and so forth. So our sequence will look like this: 1, 19, 10, 10, 10, 10, 10 .... Clearly, we can find A7, so sufficient.

Statement 2 tell us that A3=10. Well, we know that this term is the average of the two previous terms. So we know that the two previous terms must have summed to 20 to give us an average of 10 for the third term, as 20/2 =10. Thus, we have the same info as statement 1, and we can find A7[/size} This is also Sufficient.

Answer is D

Hi David,

What confused me was that the problem stated An is determined for all values of n>2 by taking the average of all terms A1 through An-1. Which made me think the average could not calculated until N>2. Can you explain?