In an Arithmetic sequence, p^(th) term is q and q^(th) term is p.Show that the n^(th) term is p+q-n.?

1 Answer
Nov 29, 2017

Please see below.

Explanation:

If first term of an arithmetic sequence is a and common difference is d, n^(th) term of arithmetic sequence is a+(n-1)d

as p^(th) term is q then

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

and as q^(th) term is p then

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

subtracting (2) from (1) we get (p-q)d=q-p i.e. d=-1

and a=q-(p-1)xx(-1)=q+p-1

and n^(th) term is a+(n-1)*(-1)

= q+p-1-n+1

= p+q-n