For a finite sequence of nonzero integers, the consecutiveness of the sequence is defined by the number of pairs of consecutive terms of the sequence for which the positive difference between the two consecutive terms is 1. What is the consecutiveness for the sequence ?
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Wait, I'm confused. Is it counting pairs where the difference is exactly 1, or the absolute difference? I got three pairs but I'm not sure if I did it right.
Positive difference means you just subtract the smaller from the larger, so it's the same as absolute value here.
This one's pretty straightforward once you know what consecutiveness means. Just go through each adjacent pair and check if the difference is 1.
Yeah I overthought it at first too. The definition is basically spelled out for you.
Is the sequence 1,4,5,6,-3,-4? So the pairs are (1,4), (4,5), (5,6), (6,-3), (-3,-4). I count three that work.
Same here. The 6 to -3 one throws you off because the difference is 9, definitely not 1.
Easy level for sure. Just need to be careful with negative numbers, -3 and -4 have a positive difference of 1.
What it tests
Your ability to spot and extend arithmetic and geometric sequences and work with recursive definitions.
Common trap
Off-by-one errors in indexing (a₀ vs a₁) or confusing an arithmetic difference with a geometric ratio.