SOLUTION: 1,7,13.....are in ap.can the sum of any terms be 175?justify

Question 994585: 1,7,13.....are in ap.can the sum of any terms be 175?justify
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
For an AP (arithmetic progression or arithmetic sequence) with first term and common difference ,
the sum of the first terms is
or
.

The sum of the first terms cannot be 175.

ONE APPROACH:
For the AP 1, 7, 13, ... , with ,
the sum of the first terms is

-->-->
The solution to that equation is not a valid , because it is not an integer:
.

ANOTHER APPROACH:
The sum of the first terms would be
That means that and are integers that multiply to yield .
We know that ,
because ,
and for each unit increase in , increases by .
That makes the possible combinations of factors of are
, which would mean , and
, which would mean .
Neither option works:
means and .
means and .

A DIFFERENT INTERPRETATION OF THE PROBLEM:
The sum of consecutive terms (not starting from ) could be :
.
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