Question of The Day29-07-2021

What is the sum of all the natural numbers between 200 and 500, which are divisible by both 3 and 4?

Correct Answer : a ) 8700

Explanation :

According to the question

The number which is divisible by both 3 and 4 is the number divisible by 12 as per the divisibility rule of 12

Immediate number after 200 which is divisible by 12 is 204

Immediate number before 500 which is divisible by 12 is 492

⇒ Numbers between 200 and 500 which are divisible by 3 and 4 are

⇒ 204, 216, 228, ………., 492

As the above series is an arithmetic progression

First term (a) of an AP = 204

⇒ Common difference (d) = 216 – 204 = 12

We know that

Number of termsn=$${Last \ term-first \ term \over Common \ difference }+1$$

⇒Number of terms (n) =$${492-204 \over 12}+1$$

⇒ 25 terms

Sum of the AP=$${n \over 2}(2a+(n-1)d)$$

Substituting the values

⇒Sum of AP=$${25 \over 2} (2*204+(25-1)*12)$$

$${25 \over 2}(408+288)$$

⇒ 8700

Hence, (a) is the correct answer.

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