
so.... since the number after .81 is 1, it doesn't really round up to .82, so is just that, 15.81.
Here 'a' corresponds to 0.
Now there are two possibilities for 'r' & 't'
Case 1.
They are on the same side to the right of 'a'
In that case 'r' corresponds to 5 & 't' corresponds to 7.
The midpoint of 'r' and 't' shall be 
Case 2.
Both are on the left of 'a'.
In that case 'r' corresponds to -5 & 't' corresponds to -7
The midpoint shall be 
Case 3.
'r' in on the right of 'a' and 't' is on the left of 'a'
So 'r' corresponds to 5 and 't' corresponds to -7
The midpoint shall be 
Case 4.
'r' is on the left of 'a' & 't' is on the right of 'a'.
'r' corresponds to -5 & 't' corresponds to 7
The midpoint shall be 
The possible coordinates of the midpoints of rt are 6, -6, 1, -1.
A_{n+1}b_{n+1} / a_{n}b_{n} =( a_{n+1} / a_{n}) * ( b_{n+1} / b_{n} ) = ( r1 ) * ( r2) =>
{a_{n}b_{n}} a geometric sequence; the common ratio is ( r1 ) * ( r2) .