In an ap if mth term is n
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In an ap if mth term is n and nth term is m show that its rth term is (m+n-r)
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Given :- am = n
an = m
Solution :-
am = n
a + ( m - 1 )d = n .... ( i )
an = m
a + ( n - 1 )d = m.... ( ii )
Sub ii from i
a + ( m - 1 )d - a - ( n - 1 )d = n - m
md - d - nd + d = n - m
md - nd = n - m
d ( m - n ) = n - m
d = - ( m - n ) / ( m - n )
d = - 1
Putting value of d in ( i )
n = a + ( m - 1 )d
n = a + ( m - 1 ) × ( - 1 )
n = a - m + 1
n + m - 1 = a
ar = a + ( r - 1 ) × ( - 1 )
ar = n + m - 1 - r + 1
ar = n + m - r
Hence proved !!
@Altaf
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