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If m times the m terms of an AP is equal to n times the n terms of the same AP .then prove that (m+n)th term of AP is zero. Bhai jaldi and jar dena

Posted by Rajan Singh 5 years, 1 month ago

CBSE > Class 10 > Mathematics

2 answers

Rajan Singh 5 years, 1 month ago

Thanks

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Gaurav Seth 5 years, 1 month ago

Let the first term of AP = a
common difference = d
We have to show that (m+n)th term is zero or a + (m+n-1)d = 0

mth term = a + (m-1)d
nth term = a + (n-1) d

Given that m{a +(m-1)d} = n{a + (n -1)d}
⇒ am + m²d -md = an + n²d - nd
⇒ am - an + m²d - n²d -md + nd = 0
⇒ a(m-n) + (m²-n²)d - (m-n)d = 0
⇒ a(m-n) + {(m-n)(m+n)}d -(m-n)d = 0
⇒ a(m-n) + {(m-n)(m+n) - (m-n)} d = 0
⇒ a(m-n) + (m-n)(m+n -1) d = 0
⇒ (m-n){a + (m+n-1)d} = 0
⇒ a + (m+n -1)d = 0/(m-n)
⇒ a + (m+n -1)d = 0

Proved!

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