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The sum of all natural numbers less than 200, that are divisible neither by 3 nor by 5 is (1)10730 (2)15375 (3)10732 (4)none of these Tell me the process.

The sum of all natural numbers less than 200, that are divisible neither by 3 nor by 5 is
(1)10730
(2)15375
(3)10732
(4)none of these
Tell me the process.

Grade:11

1 Answers

renu akunuri
37 Points
9 years ago

answer is "3"

first find the sum of  multiples of 3

that is  3+6+9+...........+198=Sn1=n(a+l)/2

we know that last term is 198 so "l"is 198 and a is 3 we have to find n value 

we know that Tn =a+(n-1)d

    198=3(n-1)3

n=66

there fore Sn1=66(3+198)/2  =6633

second find the sum of multiples of 5  similarly

we get Sn2=3900

then find the sum of multiples of 15  similarly because 15 is divisible by 3 and 5

so we get Sn3=1365

now add Sn1 and Sn2  then substract Sn3 from it

we get Sn=6633+3900-1365=9168

now we have to find sum to 199 with a=1 , d=1

we get S199=19900

now substract Sn from  S199

there fore the final answer is 19900-9168=10732

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