((n)(n+1))/2
It is my understanding that this equation is used to find the sum of n numbers. so if we are trying find 4! this equations gives use 10.
What is the equation if I wanted to find the summation of all the odd numbers or even numbers for a set?
I have seen (n/2)(2a+(n-1)d) but I am not sure what it is for.
Thanks
(Also any example problems where this could be used would be awesome)
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Question about using Equations
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Jim@StratusPrep
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You can always take the average of the first and last term and multiply that by the number of terms:
1,3,5,7,9
(1+9)/2 x 5 = 5 x 5 = 25
1,3,5,7,9
(1+9)/2 x 5 = 5 x 5 = 25
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The sum of odd numbers from 1 to some value is nice in that the sum is always the square of the number of odd values.
examples
1 = 1 (= 1^2)
1+3 = 4 (= 2^2)
1+3+5 = 9 (= 3^2)
1+3+5+7 = 16 (= 4^2)
etc.
For the sum of even numbers, we can use the n(n+1)/2 formula. All we need to do is factor out the 2 first.
For example:
2+4+6+8+10+12 = 2(1+2+3+4+5+6)
From here we can use the formula to find the sum of the integers from 1 to 6, which equal (6)(6+1)/2 = 21
So, 2+4+6+8+10+12 = 2(1+2+3+4+5+6) = 2(21) = 42
I hope that helps.
Cheers,
Brent
examples
1 = 1 (= 1^2)
1+3 = 4 (= 2^2)
1+3+5 = 9 (= 3^2)
1+3+5+7 = 16 (= 4^2)
etc.
For the sum of even numbers, we can use the n(n+1)/2 formula. All we need to do is factor out the 2 first.
For example:
2+4+6+8+10+12 = 2(1+2+3+4+5+6)
From here we can use the formula to find the sum of the integers from 1 to 6, which equal (6)(6+1)/2 = 21
So, 2+4+6+8+10+12 = 2(1+2+3+4+5+6) = 2(21) = 42
I hope that helps.
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
