2021 CSAT — Q26

Split into two interleaved sub-sequences.

Odd positions ($1,3,5,\dots$): $3,7,13,21,31,43$. First differences: $4,6,8,10,12$ — a clean run rising by $2$.

Even positions ($2,4,6,\dots$): $2,4,10,18,28,40$. First differences: $2,6,8,10,12$.

The two sub-sequences must “follow the same pattern,” so the even differences should also be $4,6,8,10,12$. Only the first difference is off ($2$ instead of $4$); the later differences $6,8,10,12$ are already correct. So the trustworthy chain is the tail $4,10,18,28,40$ (with diffs $6,8,10,12$), and the first even term is wrong.

Reconstruct it: the first difference should be $4$, so the corrected first even term is $4 - 4 = 0$. Then the even sub-sequence reads $0,4,10,18,28,40$ with differences $4,6,8,10,12$ — matching the odd pattern exactly.

The incorrect term is $2$; the correct term is $0$.

Answer: (a) 0.

When a sequence is flagged “odd and even terms follow the same pattern,” de-interleave first, then compare the two difference profiles. The odd diffs $4,6,8,10,12$ are the template; the even diffs $2,6,8,10,12$ deviate only at the head. The decisive test is which single change repairs the whole chain: setting the first even term to $0$ fixes everything, whereas editing the second term ($4\to6$) only re-breaks the next gap. Always prefer the edit that restores the entire pattern, not one that papers over one gap and opens another.