The formula is Sn=n(a1+an2){\displaystyle S_{n}=n({\frac {a_{1}+a_{n}}{2}})}, where n{\displaystyle n} equals the number of terms in the series, a1{\displaystyle a_{1}} is the first number in the series, an{\displaystyle a_{n}} is the last number in the series, and Sn{\displaystyle S_{n}} equals the sum of n{\displaystyle n} numbers., This means substituting the first term in the series for a1{\displaystyle a_{1}}, and the last term in the series for an{\displaystyle a_{n}}. When adding consecutive numbers 1 through 100, a1=1{\displaystyle a_{1}=1} and an=100{\displaystyle a_{n}=100}.

Thus, your formula will look like this: S100=n(1+1002){\displaystyle S_{100}=n({\frac {1+100}{2}})}.
 Since 100+1=101{\displaystyle 100+1=101}, you will divide 101 by 2: 1012=50.5{\displaystyle {\frac {101}{2}}=50.5}.
 This will give you the sum the consecutive number in the series. In this instance, since you are adding consecutive numbers to 100, n=100{\displaystyle n=100}. So, you would calculate 100(50.5)=5050{\displaystyle 100(50.5)=5050}. Thus, the sum of the consecutive numbers between 1 and 100 is 5,050.

To quickly multiply a number by 100, move the decimal point two places to the right.
Write the formula for finding the sum of an arithmetic series.
Plug the values into the formula.
Add the values in the numerator of the fraction, then divide by 2.
Multiply by n{\displaystyle n}.
{"src": "wikihow-all_test", "title": "How to Add Consecutive Integers from 1 to 1001"}