If you’re working on an assignment, this number will be given to you. For example, if the question asks you to find the sum of all consecutive odd numbers from 1 through 81, your ending point is 81.
For example, if your ending point is 81, 81 + 1 = 82.
For example, 82 / 2 = 41.
For example, 41 x 41 = 1681. This means the sum of all consecutive odd numbers from 1 through 81 is 1681.
Sum of first odd number = 1 Sum of first two odd numbers = 1 + 3 = 4 (= 2 x 2). Sum of first three odd numbers = 1 + 3 + 5 = 9 (= 3 x 3). Sum of first four odd numbers = 1 + 3 + 5 + 7 = 16 (= 4 x 4).
Sum of first odd number = 1. The square root of 1 is 1, and only one digit was added. Sum of first two odd numbers = 1 + 3 = 4. The square root of 4 is 2, and two digits were added. Sum of first three odd numbers = 1 + 3 + 5 = 9. The square root of 9 is 3, and three digits were added. Sum of first four odd numbers = 1 + 3 + 5 + 7 = 16. The square root of 16 is 4, and four digits were added.
For example, if you plugged 41 in for n, you would have 41 x 41, or 1681, which is equal to the sum of the first 41 odd numbers. If you don’t know how many numbers you are dealing with, the formula to determine the sum between 1 and n is (1/2(n + 1))2
This means the second number in the series will be n + 2, the third will be n + 4, etc.
For example, if you have been asked to find a series of two consecutive odd numbers that add up to 128, you would write n + n + 2 = 128.
For example, n + n + 2 = 128 simplifies to 2n + 2 = 128.
Deal with addition and subtraction first. In this case, you need to subtract 2 from both sides of the equation to get n by itself , so 2n = 126. Then deal with multiplication and division. In this case, you need to divide both sides by 2 in order to isolate n, so n = 63.
The answer to this problem is 63 and 65 because n = 63 and n + 2 = 65. It’s always a good idea to check your work by plugging your numbers back into the equation. If they don’t equal the given sum, go back and try again.
