SOLUTION: The nth term of an arithmetical progression is n and the nth term is m. Find the first term and the common difference.

Question 983883: The nth term of an arithmetical progression is n and the nth term is m. Find the first term and the common difference.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
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 being the first term,
and being the common difference,
= the nth term, so , and
= the kth term, so .
So

and
--->--->--->
The resulting formula for 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 being the first term,
and being the common difference,
the nth term is
, and
the sum of the first terms is
.
So,
-->-->-->--> , and
--->--->---> .
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