Question 711764
The difference between {{{19&1/3}}} and {{{27}}} is {{{7&2/3=23/3}}}.
It can be calculated as
{{{27-19&1/3=81/3-(19*3/3+1/3)=81/3-(57/3+1/3)=81/3-58/3=(81-58)/3=23/3=21/3+2/3=7
2/3=7&2/3}}}
It can also be calculated as
{{{27-19&1/3=27-20+20-19&1/3=7+2/3=7&2/3}}}
 
The difference between {{{27}}} and {{{57&2/3}}} is {{{30&2/3=30+2/3=90/3+2/3=92/3}}}
and that is 4 times {{{7&2/3=23/3}}}.
 
Adding {{{7&2/3=23/3}}} each time, you would add it 3 times to get the numbers to fill in the blanks, and a fourth time to get {{{57&2/3}}}.
The sequence is an arithmetic sequence
where each term is the previous one plus {{{7&2/3=23/3}}}.
The term after {{{27}}} is:
{{{27+7&2/3=27+7+2/3=34+2/3=highlight(34&2/3)=34*3/3+2/3=102/3+2/3=highlight(104/3)}}}
The next term is:
{{{34&2/3+7&2/3=34+2/3+7+2/3=41+4/3=41+1+1/3=42+1/3=highlight(42&1/3)}}}
or {{{104/3+23/3=highlight(127/3)=126/3+1/3=42+1/3=highlight(42&1/3)}}}
The next term is:
{{{42&1/3+7&2/3=42+1/3+7+2/3=49+3/3=49+1=highlight(50)}}}
or {{{127/3+23/3=150/3=highlight(50)}}}