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 :
 .
|
|
|
