Question 937656
Any term at index i would be {{{A[1]+(i-1)d}}}, for common difference of d.

Your description with the last N th term must mean, index of 3 because your sequence is given to have three terms.


To be simple, {{{a=A[1]}}}.


{{{a+(1-1)d+a+(2-1)d+a+(3-1)d=13}}}
{{{a+a+d+a+2d=13}}}
{{{highlight_green(3a+3d=13)}}}
One equation in two unknowns.


More from the description,
{{{a+(3-1)d=7}}}
{{{highlight_green(a+2d=7)}}}


Now, we have two equation in the two unknowns, a and d.


{{{system(3a+3d=13,a+2d=7)}}}


{{{system(3a+3d=13,3a+6d=21)}}}, starting with Elimination Method
E2-E1 gives.....


{{{3d=8}}}
{{{highlight(d=8/3)}}}


The middle, or term at index 2, is {{{7-8/3=21/3-8/3=highlight(13/3)}}}.



....Only three terms are in the sequence.  
"...sequence with total of the first three terms is equal to 13..."
and 
" last N th term is equal to 7."
and
"Determine the middle term of arithmetic sequence".
Those strongly imply that the last term of the sequence is at index number 3.