Mathematics - Sequence & Series Question with Solution | TestHub

If the removed numbers are $\mathrm{m}-\mathrm{d},\mathrm{m},\mathrm{m}+\mathrm{d}$, their total is $3\mathrm{m}=\mathrm{n}(\mathrm{n}+1)/2-(43/4)(\mathrm{n}-3)$. For $\mathrm{n}=19$ this gives $\mathrm{m}=6$. Positivity and $\mathrm{m}+\mathrm{d}\le 19$ allow $\mathrm{d}=2$ or 5 from the listed pairs, not $\mathrm{d}=8$. At $\mathrm{n}=23$ the computed m is not integral.