Question

find the sum of numbers from 1 to 200 which are divisible by 4

Answer 1

the series will be in A.P:
4,8,12,16,20,24......................192,196,200
a=4. ; d=4
200=4 +(n-1)4
n= 50

sum= 50/2 (4+200)
= 25×204
=5100

Answer 2

total number of number divisible by 4 between 1 to 200
first no. divisible by 4=4
last number divisible by 4 =200
In an A.P., an=a+(n-1)d
Here, an=200
a=4
d=4
we have to find n,so,
200=4+(n-1)4
196/4=n-1
49=n-1
n=50
Therefore, there are 50 numbers which are divisible by 4 between 1 and 200
Sum of an A.P.,Sn=n/2[a+an]
Here,n=50
a=4 and
an=200
Sn=50/2[4+200]
Sn=25[204]
Sn=5100
Therefore, sum of the number divisible by 4 lying between 1 and 200 is 5100.