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If m and n are natural numbers, m greater than n and sum of mth and nth term of increasing AP is 2m and their product is m square minus n square. then the( m+n)the term of arithmetic progression is

If m and n are natural numbers, m greater than n and sum of mth and nth term of increasing AP is 2m and their product is m square minus n square. then the( m+n)the term of arithmetic progression is

Grade:10

1 Answers

Arun
25750 Points
6 years ago
Dear Student
 
a +(m –1) d + a +(n –1) d = 2m
2a + (m+n –1) d = 2m
 
divide by (m+n)/2 in both the sides
 
{(m+n)/2} [2a + (m+n –1) d] = 2* m (m+n)/2
 
LHS is
sum of (m+n)th term of A.P. = m(m+n)
Hence
 
Sm+n = m(m+n)
 
Regards
Arun (askIITians forum expert)
 

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