Hi Guys - can someone please let me know the concept behind this question and how to solve.
For any positive integer n, the sum of the first n positive integres equals n(n+1)/2. What is the sum of all even integers between 99 & 301?
I understand the concept behind n(n+1)/2 and also the sum the question is asking for i.e sum of even integers between 100 & 300.
Can someone please explain the details around how to solve this?
In a set of consecutive integers the sum is equal to the number of terms * the average (or median because in consecutive terms mean = median)
Average = 301 + 99 / 2 = 200
Number of terms: 100 is the 50th even term and 300 is the 150th even term. (2 is the first even term and 100/2 = 50 or the 50th term)
150-50 + 1 = 101
Answer b: 20,200