Question

If the p th term of an Ap is q and the q th term is p,show that rth term is p+q-r

Answer 1

let a & d are the first term & common differnece respectively thenpth term = a+(p-1)d = q                       ...............(1)
\qth term = a+(q-1)d = p                     ...............(2)
Subtract (2) from (1)
a+(p-1)d - a-(q-1)d = q-p q-p = (p-q)d
d=-1
Put d = -1 in (1)
a = p + q - 1
Ar = a+(r-1)d
Substituting values of a and d
Ar = p+q - 1 +(r-1)(-1)
Ar = p+q-r+1-1
Ar = p+q-r
Hence Proved that r th term of AP = p+q-r