1
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Question

# If the sum of first n even natural numbers is equal to K times the sum of first n odd natural numbers, then K is equal to

A
1n
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B
n1n
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C
n+12n
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D
n+1n
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Solution

## The correct option is D n+1nWe know,Sn=n2[2a+(n−1)d] ......... Sum of n termsa= First termd= Common differencen= number of termsFirst n even natural numbers are :2,4,6,8......It forms an AP with first term =2 and common difference =2Sum =n2(2(2)+(n−1)2)=2n(n+1)2First n odd natural numbers are :1,3,5,7,9........It forms an AP with first term =1 and common difference =2Sum =n2(2(1)+(n−1)2)=2n22According to the question,K2n22=2⋅n2+n2⇒n2(K−1)=n∴K=n+1n

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