Question

On the first day of the play the adutorim was 1/3 the second day it was 5/12 full and on the third day it was 1/2 full. If this pattern continues how full with it be on the forth day

Answer 1

anyhow, is an arithmetic sequence, review your book on it

so.. .let's see the terms

`\bf \begin{array}{llll} term&1&2&3 \\\\ value&(1)/(3)&(5)/(12)&(1)/(2) \end{array}`

something was added to 1/3 to get 5/12
and something was added to 5/12 to get 1/2,

what the dickens was added anyway?

well, let's call it "d", or the "common difference"

you know, if something was added to the former term,
to get the latter, we can simply get their difference,
that is
subtract the former from the latter term, to get "d" :)


`\bf \begin{cases} \cfrac{5}{12}-\cfrac{1}{3}=\boxed{d} \\\\ \cfrac{1}{2}-\cfrac{5}{12}=\boxed{d} \end{cases}`

so, to get the value for the 4th term or day, simply add "d" that you found, to 1/2