Find the sum of first 28 terms?

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The discussion revolves around finding the sum of the first 28 terms of an arithmetic progression (AP) given the sums of the first 11 and 17 terms. The user struggles with the calculations, particularly with the common difference (d) resulting in a fraction. Participants clarify that the common difference in an AP can indeed be a fraction, and this does not indicate an error. The correct approach involves solving the equations simultaneously to find the values of the first term (a) and the common difference (d). Ultimately, understanding that d can be a fraction is crucial for solving the problem correctly.
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Homework Statement


sum of first 11 terms of Ap is 17 and sum of first 17 terms is 11
find the sum of first 28 terms?

Homework Equations



Sum=n/2[2a+(n-1)d]

The Attempt at a Solution


i tried solving it by using obove formula but i am not able to do so as the value of d is coming in fraction
 
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Just sub in the information and get the values for 'a' and 'd' via solving the equations simultaneously.
 


i tried but after soving the equations, value of d is coming in fraction.and the common difference cannot be a fraction number
 


nirajnishad said:
i tried but after soving the equations, value of d is coming in fraction.and the common difference cannot be a fraction number

and why not?
 


Yes, why cannot the common difference be a fraction? Are 1, 1.25, 1.5, 1.75, 2 not n AP?

Hey Niraj, keep posting your dobts on PF here, we need a lot of warming up to do!
 


nirajnishad said:
i tried but after soving the equations, value of d is coming in fraction.and the common difference cannot be a fraction number

The common difference can be a whole number, fraction, irrational number, as well as positive or negative. Finding a fraction most certainly is not an indication of an error on your part.
 
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