What is the sum of the odd numbers from 5 to 371?

Question

my choices are: 376, 34592, 34404, 68808

Answer 1

the correct answer is 34592.

the first time i used MS excel. then i wrote a database query to confirm it.

here's my SQL query:

declare @pRunningTotal as integer

declare @pMyNumber as integer


select @pMyNumber = 5
select @pRunningTotal = 0

WHILE @pMyNumber < 372
BEGIN
select @pRunningTotal = @pRunningTotal + @pMyNumber
SELECT @pMyNumber = @pMyNumber + 2
CONTINUE
END
PRINT @pRunningTotal

Answer 2

The answer is 34592. Basically the trick is to find some way of expressing it in summation notation. Consider that all odd numbers are equal to 2n-1 for some positive integer n. Then the sum of all odd numbers from 5 to 371 can be expressed as (n=3, 186)∑(2n-1). Since this is (n=1, 186)∑(2n-1) minus the sum of the first two odd numbers (1 and 3), we can write it as (n=1, 186)∑(2n-1) - 4. Using the linearity of addition to expand the summation operator, we have 2(n=1, 186)∑(n) - (n=1, 186)∑(1) - 4. Knowing that (n=1, x)∑(1) = x and (n=1, x)∑(n) = x(x+1)/2, we convert this to 2(186(187)/2) -186 - 4. Simplifying, this is 34782 - 190 or 34,592.

Answer 3

The correct answer is 34, 592.
if you have excel, put in a 5 cell A1. in the next cells down, enter the following formula =A1+2 . Copy and paste this formula down in the next 184 cells. After the bottom cell, which will show up as 371, enter this formula = Sum(A1: a184)
And there's your total. glad I could help!

Answer 4

183

Answer 5

981737