Find the sum of integers from 1 to 100 that are divisible by 3 or 5 ?

From 1 to 100, there are 33 multiples of 3 and 20 multiples of 5. Multiples of 3 are in A.P. and sum of the sequence is given by (n/2)(first term + last term), where n= no. of terms. For multiples of 3, n=33, first term= 3 and last term= 99. Similarly we calculate for multiples of 5, where n=20, 1st term= 5 and last term= 100. However there are certain number that are multiples of both 3 & 5, so we need to subtract them and those are multiples of 15. For multiples of 15, n=6, 1st term= 15, last term=90. So using the formula mentioned above for A.P., we can solve. Required Sum = (Sum of multiples of 3) + (Sum of multiples of 5) - (Sum of multiples of 15) read less

The integers from 1 to 100 which are divisible by 3=3,6,9.....99 this will form a AP with common difference 3 find the value of n using formula t(n)=a+(n-1)d u will get n=33 now find the sum of these integers for n=33 using sum formula in AP i.e S(n)=n/2[2a+(n-1)d] you will get S(n)=1683-------(1) Do the above process for 5... The integers from 1 to 100 which are divisible by 5=5,10,15........100 this will form a AP with common difference 5 find the value of n using formula t(n)=a+(n-1)d u will get n=20 now find the sum of these integers for n=20 using sum formula in AP i.e S(n)=n/2[2a+(n-1)d] you will get S(n)=1050-----------------(2) Now find the integers which r divisible by both 3 and 5.. To find the integers take L.C.M of both number(3,5) i.e 15 So first No=15 Common Ratio=15 Last No=90 So N=6 Sum=315-------------------(3) Now the required Sum=1683+1050-315 =2418 read less

Solution: Integers in between 1 and 100 which are divisible by 3 or 5. Integers divisible by 3 = 3, 6,9,12,15,.........., 99 Integers which are divisible by 5= 5,10,15,20,25,..........95 Integers divisible by 5 and 5 = 15, 30,45,60,75,90 Integers divisible by 3 or 5 = Integers divisible by + integers divisible by 5 - Integers divisible by 3 and 5 Use the above concept, find out the numbers then add them. read less