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?

Answer

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 

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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