# 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/

• -2

Given ap  = Q

aQ =  p

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

Then    ap= a +(p-1)d

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

aQ =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

ap+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 ap+Q = 0

• 53

yes pls me also explain this question

• 2

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 !

• -5

Thanks @ sudha

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