if the Pth term of an AP is Q and its Qth term is P then show that its (P+Q)th term is zero/

 Given a_p  = Q

        a_Q =  p

We know that a_n = a +(n-1)d

         Then    a_p= a +(p-1)d

                        Q=  a +(p-1)d      ...................(1)

               a_Q =a +(Q-1)d

                p= a+ (Q-1)d      .....................(2)

      SUBTRACTING (2)FROM (1 ) WE GET

Q-p = a -a +(p-1)d  -(Q-1)d

  Q-p       =  (pd -d) -(Qd -d)

    Q-p   = pd -Qd -d+d

     Q-p =  (p-Q)d

(Q -p) = -(Q-p)d

-d =(Q-p) / (Q-p)=1

d = -1   .........................(A)

Now

a_p+Q = a +(p+Q -1)d

           = a + (pd+Qd- d)

          = a+ (pd -d) +Qd

       =  a +(p -1)d + Qd

    =    ap  +Qd   (FROM 1)          

    = Q + Qd    

     = Q +Q(-1)    (FROM A)

    =Q-Q

   =0

Hence a_p+Q = 0

yes pls me also explain this question

IN AN AP IT IS GIVEN THAT Pth term isQ and Qth term is P. We have to find  (P+Q)th term .

FOR EXAMPLE -IF IN AN AP 12th TERM OF AP IS 14 AND 14th TERM OF AP IS 12 , THEN WE HAVE TO FIND (12+14) = 26th  Term of the AP

Hope it become clear to you !