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, 20:25: PM
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](https://images.topperlearning.com/topper/tinymce/cache/06f924bda6abb4236903c7251481a57d.png)
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, 23:13: PM
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