How do I solve this mushroom-related arithmetic sequence problem?

Question

I interpreted this as the side of the following arithmetic sequence starting at length 1 and increasing by $2$ every day.

$100 = 1 +(n-1)\cdot2$

$n = 99/2 +1$

$n = 50.5$

I then interpreted this as the field being full by the $51$st day from Monday. The question asks for the number of days until the field is covered including Wednesday. Therefore, I subtracted $2$ from $51$ to get $49$ days as my answer. Yet this obviously isn't an option, and the actual answer is $48$. Have I just interpreted the wording incorrectly, or is there a more fundamental mistake?

Answer 1

The First Term of the A.P should be taken as $4$ and not $1$ as $1,4,6...$ doesn't have common difference.

$$100 = 4 + (n-1)2$$ $$48 = n-1$$ $$n = 49$$

Hence the field would take $49+1 = 50$ days to be covered , but since Two days have already passed , required number of days is 48.

Answer 2

Count the number of squares formed by the mushrooms. Then we have the sequence $$1, 9,25,\dots,$$ or in other words, the squares of the odd integers, namely $(2n-1)^2.$ This also gives the area covered by the mushrooms. Since the field measures $100×100,$ it would have been covered when we have $101×101$ squares formed by the mushrooms.

This occurs on the $k$th day, so that $2k-1=101,$ or when $$k=51.$$ Indeed, it is clear from this why the answer cannot be an even number.