find the sum of all integers from 1 to 200 that are not multiple by 5
Answers
Answered by
0
First find the sum of all the terms from 1 to 200.
The sum is (200*201)/2 =20100
Now find the sum of all multiples of 5 between 1 and 200, including 1 and 200 (since it has asked to find all numbers from 1 to 200)
The multiples are 5, 10, 15........,200
Clearly they are in AP, with a=5 , d=5 and last term as 200.
So 200= a+(n-1) d = 5+(n-1)5
so 195=(n-1) 5
or n-1=39 or n=40
Sum of 40 terms of AP= (n/2)[2a+(n-1) d]
Substituting values and then solving we get the answer to be 205*20=4100
Now subtract 4100 from 20100
get the answer then
The sum is (200*201)/2 =20100
Now find the sum of all multiples of 5 between 1 and 200, including 1 and 200 (since it has asked to find all numbers from 1 to 200)
The multiples are 5, 10, 15........,200
Clearly they are in AP, with a=5 , d=5 and last term as 200.
So 200= a+(n-1) d = 5+(n-1)5
so 195=(n-1) 5
or n-1=39 or n=40
Sum of 40 terms of AP= (n/2)[2a+(n-1) d]
Substituting values and then solving we get the answer to be 205*20=4100
Now subtract 4100 from 20100
get the answer then
Similar questions