The question **"If m times of m term of an ap is equal to n times of n term of same ap show that m+n th term is zero"** is taken from class-10 ** chapter is Arithmetic Progressions Mathematics ** English-Medium

NCERT-Book ➧ class-10 ➧ Mathematics ➧ English-Medium ➧ Arithmetic Progressions ➧ Theorem For M And N Term Of Same A.P.

**Question:**

If m times of m^{th} term of an A.P. is equal to n times of n^{th} term of same A.P. Show that (m + n)^{th} term is zero.

Source:www.questionsbanks.com Last updated: 2022-10-11 21:36:33

**Answer:**

Let the first term of A.P. is a and common difference d = d,

अत: m(a_{m}) = n(a_{n})

**⇒** m[a + (m – 1)d] = n[a + (n – 1)d]

**⇒** am + m(m – 1)d = an + n(n – 1)d

**⇒** am – an + [m^{2} – m – n^{2 }+ n]d = 0

**⇒** a(m – n ) + [m^{2} – n^{2 }–( m – n)]d = 0

**⇒** a(m – n ) + [(m + n) (m – n) – ( m – n)]d = 0

**⇒** (m – n ) [a + {(m + n)– 1}]d = 0

**⇒** a + {(m + n)– 1}d = 0 ………….. (1)

a_{m + n }= a + {(m + n)– 1}d

a_{m + n }= 0 From Equation (i)

2 Questions Found on same Topics.

If m times of m^{th} term of an A.P. is equal to n times of n^{th} term of same A.P. Show that (m + n)^{th} term is zero.

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Hey! 8 Questions Found on same Chapter.

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^{th} term of an A.P. is equal to n times of n^{th} term of same A.P. Show that (m + n)^{th} term is zero.

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^{th }, q^{th} and r^{th} terms of an A.P. is a, b and c respectively, prove that : a(q – r) + b(r – p) + c(p – q) = 0 .

If t_{n} = 2n+1 then find the series (A.P).

**Which term of the sequence 114, 109, 104…………is the first negative term?**

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All chapters of NCERT Book as ncert solutions have exercise questions, textual questions and so many addtional questions like short answered questions, long answered questions and very long questions, here we included all types of questions answers format that need for a students and other stock holders like teachers and tutors. If m times of m term of an ap is equal to n times of n term of same ap show that m N th term is zero - Questions Bank is from NCERT Solutions class 10 English-Medium subject Mathematics chapter- Arithmetic Progressions Questions bank

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