If m times the mth term of an a.p is equal to n times tge nth term then prove that (m+n)th term is zero?
Answers
Answered by
0
your answer is in the attachment pls give this answer brain list mark and give me thanks
Attachments:
Answered by
0
Answer:
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!
Similar questions
Social Sciences,
6 months ago
Math,
6 months ago
Computer Science,
6 months ago
Geography,
1 year ago
Physics,
1 year ago
Biology,
1 year ago
Math,
1 year ago