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If m times mth term of an AP is equal to n times nth term, then show that (m+n)th term of the AP is zero

Posted by Aradhana Hota 5 years, 4 months ago

CBSE > Class 10 > Mathematics

3 answers

? Pranali.A.P ? 5 years, 4 months ago

1Thank You

Tanmay Bagade 5 years, 4 months ago

1Thank You

? Pranali.A.P ? 5 years, 4 months 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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CBSE > Class 10 > Mathematics