Question

if the pth term of an A. P. is q, and the qth term is p, show that rth term is p+q-r?

Answer 1

a + (p-1)d = q------------- 1
a + (q-1)d = p------------- 2
subtracting 2 from 1, we get:
[(p-1) - (q-1)]d = q-p
(p-q)d = q-p
d = -1
using  (1), a+(p-1)* -1 = q
hence, a -p+1 = q
a= q+p-1----------------------------------(3)
 now, rth term = a+(r-1)* -1
using (3), tr = q+p-1-r+1 = q+p-r
                Hence the proof...