The pattern repeats in a finite order. The \(1st, 5th, 9th\) term and so on are \(1\)

Similarly, \(2nd, 6th, 10th\) term and so on are \(2\)

\(-3\) and \(-4\) also repeat in a difference of 4 numbers.

Since all the numbers repeat in a difference of \(4\) we can find the position of given term by finding the remainder when divided by \(4\)

For qty A

when \(49\) is divided by \(4\) remainder is \(1\) so the \(49th\) term has value of \(1\) from the \(1st\) number in the sequence

similarly when \(51st\) term is divided by \(4\) the remainder is \(3\) so the the \(51st\) term has the value \(-3\) which is the third number in the sequence

sum of \(-3\) and \(1 = -2\)

For qty B

when \(50\) is divided by \(4\) remainder is \(2\) so the \(50\)th term has value of \(2\) from the 2nd number in the sequence

when \(52\) is divided by\(4\) remainder is \(0\) so the \(52\)nd term has value of \(-4\) from the 4th number in the sequence

\(2 + -4 = -2\)

option C

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This is my response to the question and may be incorrect. Feel free to rectify any mistakes