Answer
10,100
Work Step by Step
Method 1- -
2 + 4 + 6 + 8 + 10 . . . . .+ 200
First term $a_{1}$ = 2
Common difference d = 2
Sum of n terms = $\frac{n}{2}$($a_{1}$ + $a_{n}$)
Sum of first 100 positive even integers = $\frac{100}{2}$(2 + 200)
= 100$\times$101 = 10100
Method 2- -
2 + 4 + 6 + 8 + 10 . . . . .+ 200 = 2(1 + 2 + 3 + 4 + 5 +......+100)
First find sum of (1 + 2 + 3 + 4 + 5 +......+100) and then multiply the sum by 2
First term of series $a_{1}$ = 1
Common difference in series d = 1
Sum of n terms = $\frac{n}{2}$($a_{1}$ + $a_{n}$)
Sum of first 100 natural numbers= $\frac{100}{2}$(1 + 100)
= 50$\times$101 = 5050
2 + 4 + 6 + 8 + 10 . . . . .+ 200 = 2(1 + 2 + 3 + 4 + 5 +......+100) = 2 $\times$ 5050 = 10,100
