Question

Find the sum of all even numbers between 1 and 100.

A. 2020
B. 2021
C. 2450
D. 2451
W/ solution!!!

Answer 1

Step-by-step explanation:

The first even number between 1 &100 is 2

the last even number between 1 & 100 is 98

so,the ap is 2,4,6,8,.......98

difference (d)=2

first term(a)=2

last term(l)=98

n=?

so,

n=l-a/d+1

n=98-2/2+1

n=96/2+1

n=48+1

n=49

and,

sum of terms=n/2*[2a+(n-1)d]

=49/2*[2(2)+(49-1)(2)]

=49/2*[4+48(2)]

=49/2*[4+96]

=49/2*[100]

=49*50

=2,450

so, therefore the correct option is (c)

Answer 2

Answer:

2450

Step-by-step explanation:

No. of even numbers between 1 and 100=49

Sum of even numbers=49/2{2×2+(49-1)2}

=49/2{4+48×2}

=49/2×100

=49×50

=2450