The sum of 6 consecutive odd numbers is 20. What is the fourth number in this sequence?
1 Answer
There is no such sequence of
Explanation:
Denote the fourth number by
Then the six numbers are:
#n-6, n-4, n-2, color(blue)(n), n+2, n+4#
and we have:
#20 = (n-6)+(n-4)+(n-2)+n+(n+2)+(n+4)#
#color(white)(20) = (n-6)+5n#
#color(white)(20) = 6n-6#
Add
#26 = 6n#
Divide both sides by
#n = 26/6 = 13/3#
Hmmm. That is not an integer, let alone an odd integer.
So there is no suitable sequence of
What are the possible sums of a sequence of
Let the average of the numbers be the even number
Then the six consectuvie odd numbers are:
#2k-5, 2k-3, 2k-1, 2k+1, 2k+3, 2k+5#
Their sum is:
#(2k-5)+(2k-3)+(2k-1)+(2k+1)+(2k+3)+(2k+5) = 12k#
So any multiple of
Perhaps the sum in the question should have been