SOLUTION: If the average of 19 consecutive numbers is 545, what is the least of these numbers?

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Question 925304: If the average of 19 consecutive numbers is 545, what is the least of these numbers?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Re TY: ...Knowing the Average of the consecutive numbers ...
We are Finding the 1st term of an Arithmetic Sequence(d=1) of 19 terms
...
average of 19 consecutive numbers is 545
sum%2F19+=+545 Defn of Average
sum+=+19%2A545
sum of the Numbers = 10,355
.........
Considering a Arithmetic Sequence Sum of n terms
S%5Bn%5D+=%28+n%2F2%29%28a%5B1%5D%2Ba%5Bn%5D%29

%28a%5B1%5D+%2B+a%5B19%5D%29+=+%282%2F19%29%2810355%29
a1 + a19 = 1090
......
Considering a Arithmetic Sequence(d=1): nth term
a%5Bn%5D+=+a%5B1%5D+%2B+%28n-1%29d
a19 = a1 + 18
....
2a1 + 18 = 1090
a1 = (1090-18)2
a1 = +highlight_green%28536%29
..........
and...checking
S19 = 19/2(536 + 554) = 10,355
10355%2F19+= 545