Question

Find the sum of all 3 digit numbers which are divisible by 3 but not 6

Answer 1

Hello!!

3 digit number starts from 100,101.. and ends at 999.

Arithmetic progression can be used to find all 3 digit number that is divisible by 3 and not by 6.

The 1st 3 digit number that is divisible by 3 and not by 6 is 105. The next numbers are 111,117,123.. (previous number added with 6).The last number is 999.

nth term of an arithmetic progression-

tn = a + (n – 1)d

where tn- nth term(999)

a =the first term (105)

d= common difference(6)

999=105+(n-1)6

894=(n-1)6

n=150

The addition of series is given by-

Sn= n/2*(a+tn)

= 1502(105+999)

= 75 (1104)

= 82800 .

So there are only 150 3 digit numbers that is divisible by 3 and not by 6 and there addition is 82800.

Hope it helps you...

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