The sum of the first 10 terms of an AP is the same as the sum of its first 5 terms, then the sum of its 15th term will be _______(a) 1(b) 0(c) 2(d) 3The question was posed to me in semester exam.My question is based upon Sum of N Terms of Arithmetic Progression in section Arithmetic Progressions of Mathematics – Class 10

The sum of the first 10 terms of an AP is the same as the sum of its f

1.	The sum of the first 10 terms of an AP is the same as the sum of its first 5 terms, then the sum of its 15th term will be _______(a) 1(b) 0(c) 2(d) 3The question was posed to me in semester exam.My question is based upon Sum of N Terms of Arithmetic Progression in section Arithmetic Progressions of Mathematics – Class 10
Answer» Right option is (B) 0 For explanation I would say: The SUM of the first 10 TERMS of an AP is the same as the sum of its first 5 terms S10 = S5 \(\frac {10}{2}\) (2a + (10 – 1)d) = \(\frac {5}{2}\) (2a + (5 – 1)d) 5(2a + 9d) = \(\frac {5}{2}\) (2a + 4d) 5(2a + 9d) = 5(a + 2d) (2a + 9d) = (a + 2d) 2a – a = 2d – 9d a =– 7d S15 = \(\frac {N}{2}\) (2a + (n – 1)d) = \(\frac {15}{2}\) (2a + (15 – 1)d) = \(\frac {15}{2}\) (2a + 14D) = 15(a + 7d) = 15(-7d + 7d) = 0

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