Got this question wrong at first because i couldn't make out that the K is not the number of terms in this series, its just the last term in it.

We already know the formula of the

sum of first N odd integers = \(N^2\)So, \(N^2\) = 441

N = 21

Hence, the number of terms in this series is 21.

At this point i realised that N and K are different here, for eg:

1,3,5,7 => N=4; K=7

1,3,5,7,9,11,13 => N=7; K=13

We can see that, \(K = 2N-1\)

since we have N=21 for this series, we can find out K

\(K=2*21 - 1\)

\(K=41\)

Side note (not quite reqd here but could be helpful in similar questions): "Sum of odd number of odd numbers is odd and Sum of even number of odd numbers is even"

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