Question

13. A) What is the least three digit number which is a multiple of 6?
B) Find the sum of all three digit numbers which are Multiples of 6.​

Answer 1

Answer:

(A) 108 is the three digit number

Answer 2

first three digit number divisible by 6=102.

last three digit number divisible by 6=996.

=>102+108+114..+996

clearly,this series is in A.P

First term a =102,common difference d =108minus 102=6,last term tn=996 now

we know that tn=a+(n-1)*6

=>996=102+(n-1)*6

=>996=102+6n-6

=>996=96-6n

=>1092=6n

=>n=150

now,

sum of the required series an =n/2(a+1)

=>(150/2)(102+996)

=>75(1098)

=>82350

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