If the p th term of an AP is q and the q th term of an AP is p, than prove that the n th term is (p+q-n).
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q=a+(p-1)d
p=a+(q-1)d
by subtracting both the equations
q-p=d(p-1-q+1)
q-p=d(p-q)
d = -1
if we put the value of d in any of the above equation
a=q+p-1
nth term = a+(n-1)d
=q+p-1+ (n-1) -1
=q+p-1-n+1
=q+p-n
=(p+q-n)
p=a+(q-1)d
by subtracting both the equations
q-p=d(p-1-q+1)
q-p=d(p-q)
d = -1
if we put the value of d in any of the above equation
a=q+p-1
nth term = a+(n-1)d
=q+p-1+ (n-1) -1
=q+p-1-n+1
=q+p-n
=(p+q-n)
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