Given:
First five consecutive positive integers.
To find:
The sum of the first 5 consecutive positive integers.
Sum of the first n consecutive whole numbers.
Solution:
First five consecutive positive integers are 1, 2, 3, 4 and 5.
Sum of these numbers is
Therefore, the sum of the first 5 consecutive positive integers is 15.
First n consecutive whole numbers are 0, 1, 2, 3,..., (n-1). These numbers are in AP.
Here, first term is 0 and common difference is 1.
Sum of n terms of an AP is
where, a is first term and d is common difference.
Substitute a=0 and d=1 in the above formula.
Sum of first 5 consecutive positive integers is equal to the sum of first 6 consecutive whole number because in whole numbers 0 is extra number.
For n=6,
The sum of the first 5 consecutive positive integers is 15.
So, the sum of (n-1) consecutive positive integers is