Question

What Is The Sum Of All Even Integers Between 99 And 301 a) 20200 b) 20000 c) 40400 d) 40000?

Answer 1

Answer:

a

Step-by-step explanation:

We need to find sum of all even integers between 99 and 301

So 100 would be least such integer and 300 would be greatest of that type

So series will look like

100,102,104,106,.......,300

Now if one knows basic concepts of an arithmetic progression he would be delighted to see such type of questions

Here First term,a=100

Common difference,d=102-100=104-102=.....=2

Last term,l=300

Now we have a relationship among a,d and I

l=a+(n-1)*d

where n is number of terms

300=100+(n-1)*2

200=(n-1)*2

(n-1)=100

n=101

Now we have to find sum of these 101 terms

Sum of n terms of an arithmetic progression is given by Sn

Sn=n*(2*a+(n-1)*d)/2

S101=101*(2*100+(101-1)*2)/2

S101=101*(200+100*2)/2

S101= 101*400/2

S101=20200

Sum of all even integers between 99 and 301 is therefore 20200