Quote:
The sum of the first 100 positive integers is how much greater than the sum of the first 80 positive integers?
Step 1: Understanding the questionSum of consecutive integers = Average * number of terms
Average of consecutive integers = \(\frac{(first Term + Last Term)}{2}\)
Step 2: Calculationsum of the first 100 positive integers = \(\frac{(1+100)}{2}\) * 100 = 101 * 50 = 5050
sum of the first 80 positive integers = \(\frac{(1+80)}{2}\) * 80 = 81 *40 = 3240
Difference between sum of the first 100 positive integers and sum of the first 80 positive integers = 5050 - 3240 = 1810
D is correct