Question

if the p term of an Ap is q and q term is p, then prove that its n term is (p+q-n)

Answer 1

Let the first term be a and the common difference be d.
Given p th term=q
=>a+(p-1)d=q ... 1
And, q th term =p
=>a+(q-1)d=p ... 2
Subtracting 2 from 1,we get
(p-q) d=q-p
=>d=q-p/p-q
=q-p/-(q-p) =-1
So d=-1
Substituting its value in 1,
a+(p-1)-1=q
=>a-p+1=q
=>a=q+p-1
So n th term=a+(n-1) d
=q+p-1+(n-1)-1
=q+p-1-n+1
=q+p-n (proved)