Q. 174.5( 4 Votes )

# Mark the correct alternative in the following:

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

A.

B.

C.

D.

Answer :

Let first A.P is 2,4,6…

So, a=2 and d=4-2=2

Let S_{1} denotes the sum of n even numbers

Now, sum of n term is given by,

Let second A.P is 1,3,5…

So, a=1 and d=3-1=2

Let S_{2} denotes the sum of n odd numbers

Now, sum of n term is given by,

Now, given that S_{1}=kS_{2}

∴n(n+1)=kn^{2}

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