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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