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CBSE Class 10 Answered

The mth term of an AP is n and the nth term is m. Find the rth term of the AP.
Asked by latayadav23 | 17 Oct, 2023, 08:25: PM
answered-by-expert Expert Answer
Let a be the first term and d be the common difference of Arithmetic progression.
 
mth term :-  a + ( m -1 ) d = n \ \...................... (1)
 
nth term :-  a + ( n-1 ) d = m ........................(2)
 
By subtracting eqn.(2) from eqn.(1) , we get
 
begin mathsize 14px style left parenthesis space m space minus space n space right parenthesis space d space equals space left parenthesis space n space minus space m space right parenthesis end style
 
hence we get , d = -1
 
By substituting  d = -1  in eqn.(1) , we get  a = ( m + n -1 )
 
rth term :-  a + ( r -1 ) d =  ( m + n -1 ) + ( r-1 ) (-1)  = ( m+n-r )
Answered by Thiyagarajan K | 17 Oct, 2023, 11:13: PM

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