Answer
6480
Work Step by Step
Method 1- -
Sum of first 80 positive even integers = 2 + 4 + 6 + 8 + 10 . . . . .+ 160
First term $a_{1}$ = 2
Common difference d = 2
$60^{th}$ term = 160
Sum of n terms = $\frac{n}{2}$($a_{1}$ + $a_{n}$)
Sum of first 80 positive even integers = $\frac{80}{2}$(2 + 160)
= 40$\times$162 = 6480
Method 2- -
2 + 4 + 6 + 8 + 10 . . . . .+ 160 = 2(1 + 2 + 3 + 4 + 5 +......+80)
First find sum of (1 + 2 + 3 + 4 + 5 +......+80) and then multiply the sum by 2
First term of series $a_{1}$ = 1
Common difference in series d = 1
$80^{th}$ term = 80
Sum of n terms = $\frac{n}{2}$($a_{1}$ + $a_{n}$)
Sum of first 80 natural numbers= $\frac{80}{2}$(1 + 80)
= 40$\times$81 = 3240
2 + 4 + 6 + 8 + 10 . . . . .+ 160 = 2(1 + 2 + 3 + 4 + 5 +......+80) = 2 $\times$ 3240 = 6480
