Question 983883
TYPO!
"The
nth term of an arithmetical progression is n     and the
nth term is m."


So, the nth term is n = m ,
and we do not have enough information about the rest of the arithmetic progression?
I guess the problem should read differently,
and I believe I am a good guesser,
but from so little information, all I can manage is some wild guesses.


GUESS # 1:
Maybe it should read 
"The nth term of an arithmetical progression is n,
and the kth term is m."
Maybe with a number instead of k, or maybe k is m.
Then, with {{{a[1]}}} being the first term,
and {{{d}}} being the common difference,
{{{a[n]=a[1]+d*(n-1)}}}= the nth term, so {{{n=a[1]+d*(n-1)}}} , and
{{{a[k]=a[1]+d*(k-1)}}}= the kth term, so {{{m=a[1]+d*(k-1)}}} .
So
{{{n-m=(a[1]+d*(n-1))-(a[1]+d*(k-1))}}}
{{{n-m=a[1]+d*(n-1)-a[1]-d*(k-1)}}}
{{{n-m=d*(n-1)-d*(k-1)}}}
{{{n-m=d*(n-1-(k-1))}}}
{{{n-m=d*(n-1-k+1)}}}
{{{n-m=d*(n-k)}}}
{{{highlight(d=(n-m)/(n-k))}}} and
{{{System(n=a[1]+d*(n-1),d=(n-m)/(n-k))}}}--->{{{n=a[1]+((n-m)/(n-k))*(n-1)}}}--->{{{n=a[1]+(n-m)*(n-1)/(n-k)}}}--->{{{highlight(a[1]=n-(n-m)*(n-1)/(n-k))}}}
The resulting formula for {{{a[1]}}} is messy,
but I do not see a way to make it look simple.


GUESS # 2:
Maybe it should read 
"The sum of the first n terms of an arithmetical progression is n,
and the nth term is m."
Then, with {{{a[1]}}} being the first term,
and {{{d}}} being the common difference,
the nth term is
{{{a[n]=a[1]=d*(n-1)=m}}} , and
the sum of the first {{{n}}} terms is
{{{n*(a[1]+a[n])/2=n*(a[1]+m)/2=n}}} .
So,
{{{n*(a[1]+m)/2=n}}}-->{{{(a[1]+m)/2=n/n}}}-->{{{(a[1]+m)/2=1}}}-->{{{a[1]+m=2}}}-->{{{highlight(a[1]=2-m)}}} , and
{{{system(a[1]+d*(n-1)=m,a[1]=2-m)}}}--->{{{2-m+d*(n-1)=m}}}--->{{{d*(n-1)=2m-2}}}--->{{{highlight(d=(2m-2)/(n-1))}}} .