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 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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