If the mth term of an A.P is n and nth term is m, find the rth term.

let a be the first term,d be common diff.

Tn=a+(n-1)d=m

Tm=a+(m-1)d=n

=>n-a=(m-1)d

=>d=n-a/m-1-----------(1)

now d also equal to m-a/n-1

=>m-a/n-1=n-a/m-1

on solving for a,we get a=m+n-1-------------(2)

put eqn2 in eqn1..we get d=-1

=>Tr=a+(r-1)d

puttin values of a and d,we get Tr = m+n-r

m+n-r is answer

i wrote answers but this disgusting site on its own log outs ma accounts so lost whole expaination

telling in short

solve equation of am and an and get value of a and d d comes -1 and put ar=a+(n-1)d

and put values of a and d to get answers

thnx

yr. ansr is correct!

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so next time i can ask qustns frm u!