Question

Find the sum of all 3 digit natural number which are divisble 3but not divisible by 6

Answer 1

Answer: 82800

Step-by-step explanation:

All 3 digit natural numbers which are divided by 3 forms an AP with first term 102 and nth term 999 with a common difference 3, where we need to find the value of n

nth term 999⇒a+(n-1)d=999

⇒ 102+(n-1)3=999

⇒3n=999-102+3=900

⇒n=300

So sum of 300 terms of this AP is 300/2(102+999) =165150

Similarly all 3 digit natural numbers which are divided by 6 forms an AP with first term 102 and nth term 996 with common difference 6

nth term 996 ⇒ 102+(n-1)6=996

⇒6n = 996 - 102 + 6 =900

⇒n=150

So sum of 150 terms of this AP is 150/2(102+996) = 82350

So Sum of all 3 digit natural numbers which are divisible by 3 but not by 6 = sum of all numbers divisible by 3 - sum of all numbers divisible by 6

=165150-82350

=82800