SOLUTION: what is the sum of the first 1,000 consecutive odd numbers?

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Question 259364: what is the sum of the first 1,000 consecutive odd numbers?
Found 4 solutions by Fombitz, stanbon, Alan3354, CharlesG2:
Answer by Fombitz(32388) About Me  (Show Source):
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The first 1000 consecutive odd numbers run from 1 to 1999.
The first 1000 consecutive even numbers run from 2 to 2000.
The sum of numbers from 1 to 2000 is,
N=%282000%29%282001%29%2F2=2001000
Each even number is 1 greater than each odd number like
1, 2
3, 4
Each even number is an odd number plus one.
So then the total sum is the sum of all the odds twice plus 1000.
2%2AOS%2B1000=2001000
2%2AOS=2000000
OS=1000000
ES=1001000
where OS is odds summed from 1 to 1999 and ES is the evens summed from 2 to 2000.

Answer by stanbon(75887) About Me  (Show Source):
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what is the sum of the first 1,000 consecutive odd numbers?
---
1 + 3 + 5 + (2n-1) +.....+ (2*1000-1)
---
The 1000th term is 1999
----
Formula: S(n) = (n/2)(a(1) + a(n))
-------------------
S(1000) = (1000/2)(1+1999)
= 500(2000)
= 1,000,000
==================
Cheers,
Stan H.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
What is the relevance of consecutive?
How does that differ from the first 1000 odd numbers?
---------------------
The first 1000 consecutive odd numbers run from 1 to 1999.
Add the extremes:
1 + 1999 = 2000
3 + 1997 = 2000
All the pairs add to 2000
There are 500 pairs.
500*2000 = 1,000,000

Answer by CharlesG2(834) About Me  (Show Source):
You can put this solution on YOUR website!
what is the sum of the first 1,000 consecutive odd numbers?
consecutive numbers both even and odd table
+sum%28+i%2C1%2Cn+%29+=+%28n%28n%2B1%29%29%2F2+
(the sigma sign you see means to sum from n=0 to n=n)
n n(n+1)/2
1 1
2 3
3 6
4 10
5 15
10 55
100 5050
1000 500500
2000 2001000
now what is an odd number? an odd number can not be divisible by 2, we need to come up with a formula that only comes up with an odd number
2n-1 is an odd number where n=1,2,3,4,...
n=1 ---> 2n-1=2-1=1
n=2 ---> 2n-1=4-1=3
n=3 ---> 2n-1=6-1=5
n=4 ---> 2n-1=8-1=7
and so on to...
n=1000 --->2n-1=2000-1=1999
we want to sum the first 1000 consecutive odd numbers though
1+3=4=2^2
4+5=9=3^2
9+7=16=4^2
16+9=25=5^2
see what is happening here?
+sum%28+i%2C1%2C2n-1+%29+=+n%5E2+
n 2n-1
1 1
2 3
3 5
4 7
5 9
10 19
100 199
1000 1999
n^2 plug in 1000 for n
1000^2=1000000 or 1 million
the sum of the first 1,000 consecutive odd numbers is 1 million