Find sum of all odd numbers between 70 and 150
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Answer:
How do I calculate the the sum of all the odd numbers between 50 and 150? As well as the sum of the even numbers from 50 to 150, inclusive.
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We can also use S = n[2a + (n-1)d]/2 to calculate both answers
where n = number of terms, a = first term, and d = difference between terms.
There are 101 terms/numbers between 50 and 150,
and we can see the start and end numbers of 50 and 150 respectively are even,
therefore there must be 1 more positive number than negative number.
That makes 51 positive numbers and 50 negative numbers from 50 to 150.
So the sum of positive numbers from 50 to 150 is
S = n[2a + (n-1)d]/2
S= 51[2(50) + (50)2]/2
S=51(200)/2
S=5100
Likewise for the negatives,
S = n[2a + (n-1)d]/2
S= 50[2(51) + (49)2]/2
S=50(200)/2
S=5000
To chec
What is the sum of odd integers between 50 and 150?
What is the sum of all odd numbers between 100 and 400?
What is the sum of odd numbers from 1 to 50? What is the sum of even numbers from 1 to 50?
How many even numbers are there between 50 and 100 (both inclusive)?
What is the sum of all natural numbers from 50-150?
First we find the sum of all of the integers up to 75 (half of 150) by pairing integers as follows:
1+75 = 76
2+74 =76
3+73=76
.. + .. =76
37+39=76
There are 37 such pairs of integers with 38 remaining unpaired so the sum of the integers up to 75 is 37*76 +38 = 75*76/2 = 2850.
This is a specific case of the general expression for S, the sum of the first N integers given by S=N(N+1)/2.
The sum of the even integers up to 150 is just twice the sum of all of the integers up to 75. Therefore the sum of the even integers up to 150 is 2*2850 = 5700.
The sum of the even integers up to 48 is twice the sum of the integers up to 24 Therefore the sum of the even numbers up to 48 is 2*24*25/2 = 25*24=600.
Therefore the sum of the even integers from 50 to 150 inclusive is 5700–600=5100.
The sum of the odd integers up to 150 is obtained by subtracting the sum of the even integers up to 150 from the sum of all the integers up to 150.
The sum of all of the integers up to 150 is 150*151/2 = 11325.
The sum of all of the odd integers up to 150 is therefore 11325–5700=5625.
The sum of the odd integers up to 50 is equal to the sum of all of the integers up to 50 minus the sum of the even integers up to 50. This is 50*51/2 - 600 = 1275–600 = 675.
Therefore the sum of the odd integers from 50 to 150 is 5625–675=4950.
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