Help, is my answer correct? Recursive equations?

Question

anonymous · Answer

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anonymous · Answer

Notice the finite differences between our days.

From day 1 to 2, we gain 4 cells.
From day 2 to 3, we gain 5.
From 3 to 4, we gain 6.

Which equation there looks like closest match? :-)
Well 4 = 2 + 2, 5 = 3 + 2, 6 = 4 + 2, etc. so the difference between $a_n$ and $a_{n-1}$ is just $n+2$. Writing out in math terms,$$a_n-a_{n-1}=n+2\a_n=a_{n-1}+(n+2)$$

anonymous · Answer

I'm really not getting it. :( The pattern I understand, just not how the equation works. But it's the third one?

anonymous · Answer

Try plugging numbers for $n$... for $n=2$, we're saying $a_2=a_1+(2+2)=a_0+4$, so we *gain* 4 from day 1 to day 2. Similarly, for $n=3$ we're saying $a_3=a_2+(3+2)=a_2+5$ , so we *gain* 5 from day 2 to 3 (and we do -- from 5 cells to 10 cells).

anonymous · Answer

Oops, where I wrote $a_0$ I intended $a_1$.

anonymous · Answer

Okay, I'll try.

anonymous · Answer

I still don't understand. :\ I'm sorry.