Question

If pth term is q and qth term is p of an A.P. then its rth term is​

Answer 1

the answer is nothing but r

Answer 2

APQ,

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

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

Subtract 2 from 1,

That gives,

=>(p-1)d-(q-1)d= q-p

=>d(p-1-q+1)= q-p

=>d(p-q)= -p+q

=>d= -p+q/p-q= -1

Substitute this value in eq^n 1:

=>a+ (p-1) ( -p+q )/p-q= q

=>a+ (p-1) [ -1(p-q)/p-q] = q

=>a-p+1=q

=>a= p+q-1

rth term is,

ar= a+(r-1)d

(substitute p+q-1 for a )

ar= p+q-1(r-1) -1

=> p+q-1-r+1

So, rth term is p+q-r.....