saintdora wrote:
Need help. Am I to assume the consecutive 11 integers are evenly spaced by 1 unit? Why not assume its spaced by 2 units? (Please note, I know it's much easier to space by 1 unit and I did this when solving this problem and got it correct ![:-)]( "Smile")
My objective here is to help me deeply understand the question).
For instance, statement 1:
(1) The objective of question is to determine the value of the 6th term of the consecutive 11 integers, provided the avg=median concept
(2) Assuming consectuive integers are spaced by 2 units (rather than 1); the SUM FORMULA of the first 9 integers could be written as (n) + (n+2) + (n+4) + ... + (n+16) = 9n + 72
(3) Plug SUM FORMULA into AVG FORMULA to find the value of n --> (9n + 72)/9=7 --> (9n + 72)=63 --> n=-1
(4) The 6th term is defined as (n+14) --> (-1)+10 = 9
The value for the answer I found when spacing by 2 units is 9, as opposed to spacing by 1 and getting the answer value of 8.
.... Bunuel post states, Mean(=median of first 9 terms=5th term)*# of terms=63 --> x59=63x59=63 --> x5=7x5=7 --> x6=7+1=8, which seems soundproof to me. Nonetheless, I'd love to understand how to select the unit spacing.
Simply put, why can there be only one, unique set of 9 consecutive integers to total 63? Am I to assume the spacing is by 1 unit? and if so, how do I know that when taking the test? Many thanks and I appreciate your help.
My objective here is to help me deeply understand the question).For instance, statement 1:
(1) The objective of question is to determine the value of the 6th term of the consecutive 11 integers, provided the avg=median concept
(2) Assuming consectuive integers are spaced by 2 units (rather than 1); the SUM FORMULA of the first 9 integers could be written as (n) + (n+2) + (n+4) + ... + (n+16) = 9n + 72
(3) Plug SUM FORMULA into AVG FORMULA to find the value of n --> (9n + 72)/9=7 --> (9n + 72)=63 --> n=-1
(4) The 6th term is defined as (n+14) --> (-1)+10 = 9
The value for the answer I found when spacing by 2 units is 9, as opposed to spacing by 1 and getting the answer value of 8.
.... Bunuel post states, Mean(=median of first 9 terms=5th term)*# of terms=63 --> x59=63x59=63 --> x5=7x5=7 --> x6=7+1=8, which seems soundproof to me. Nonetheless, I'd love to understand how to select the unit spacing.
Simply put, why can there be only one, unique set of 9 consecutive integers to total 63? Am I to assume the spacing is by 1 unit? and if so, how do I know that when taking the test? Many thanks and I appreciate your help.
When we see "consecutive integers" it ALWAYS means integers that follow each other in order with common difference of 1: ... x-3, x-2, x-1, x, x+1, x+2, ....
For example:
-7, -6, -5 are consecutive integers.
2, 4, 6 ARE NOT consecutive integers, they are consecutive even integers.
3, 5, 7 ARE NOT consecutive integers, they are consecutive odd integers.
So, not all evenly spaced sets represent consecutive integers.