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#.?

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Answer 1 · 2017-11-29T14:42:50

Please see below.

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#