In the series,6, 4, 1, 2, 2, 8, 7, 4, 2, 1, 6 | vedclass

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(C) To find pairs of alternate numbers with a difference of $2$,we examine the sequence by skipping one number at a time.The sequence is: $6, 4, 1, 2,

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Three

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(C) To find pairs of alternate numbers with a difference of $2$,we examine the sequence by skipping one number at a time.The sequence is: $6, 4, 1, 2, 2, 8, 7, 4, 2, 1, 6, 3, 8, 6, 2, 1, 7, 1, 4, 1, 3, 2, 8, 6$.Pairs of alternate numbers $(a_n, a_{n+2})$ are:$(6, 1), (4, 2), (1, 2), (2, 8), (2, 7), (8, 4), (7, 2), (4, 1), (2, 6), (1, 3), (6, 8), (3, 6), (8, 2), (6, 1), (2, 7), (1, 1), (7, 4), (1, 1), (4, 3), (1, 2), (3, 8), (2, 6)$.Now,we calculate the absolute difference $|a_n - a_{n+2}|$ for each pair:$|6-1|=5, |4-2|=2, |1-2|=1, |2-8|=6, |2-7|=5, |8-4|=4, |7-2|=5, |4-1|=3, |2-6|=4, |1-3|=2, |6-8|=2, |3-6|=3, |8-2|=6, |6-1|=5, |2-7|=5, |1-1|=0, |7-4|=3, |1-1|=0, |4-3|=1, |1-2|=1, |3-8|=5, |2-6|=4$.The pairs with a difference of $2$ are $(4, 2), (1, 3),$ and $(6, 8)$.Thus,there are $3$ such pairs.

In the series,$6, 4, 1, 2, 2, 8, 7, 4, 2, 1, 6, 3, 8, 6, 2, 1, 7, 1, 4, 1, 3, 2, 8, 6$,how many pairs of alternate numbers have a difference of $2$?

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