In an arithmetic progression (S_{14}=497) and (S_{13}=429). What is the (14)th term?

(68)

The sum of the first 14 terms includes the first 13 terms plus the fourteenth term. Therefore, subtracting the two consecutive sums isolates that final term: \\(a_{14}=S_{14}-S_{13}\\). Substituting the given values gives \\(a_{14}=497-429=68\\). This property works for any sequence when consecutive partial sums are known, and it is especially useful in arithmetic-progression questions.

The difference is positive, so the fourteenth term is 68, not one of the nearby values caused by an arithmetic subtraction error. There is no need to find the first term or common difference because the required term follows directly from the two sums. Hence option C is correct. Options A, B, and D do not equal the difference between the given consecutive sums.

This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the sum of the first $n$ terms of an AP.