Find the sum of first 28 terms?

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Homework Help Overview

The problem involves finding the sum of the first 28 terms of an arithmetic progression (AP), given the sums of the first 11 and 17 terms. The original poster expresses difficulty in solving for the common difference due to it resulting in a fraction.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss substituting known values into the formula for the sum of an AP to derive the first term and common difference. There are questions about the validity of a fractional common difference and whether it can exist in an AP.

Discussion Status

The discussion is ongoing, with some participants providing guidance on the nature of common differences in APs, suggesting that a fractional value is acceptable. Multiple interpretations regarding the nature of the common difference are being explored.

Contextual Notes

There is a concern raised about the common difference being a fraction, which some participants challenge, indicating a need to clarify assumptions about the properties of arithmetic progressions.

nirajnishad
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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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