Question

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

Answer 1

i think the rth term will be r

Answer 2

Answer

The rth term of the AP is p+q-r

Step-by-step explanation:

Let general nth term of the A.p is given by

$a_n=a+(n-1)d$

where  

• $a_n$ is the nth term of the A.P

• a is the first term
• d is the common difference of the A.P

According to question we have

$q=a+(p-1)d\\\\p=a+(q-1)d$

Solving above equation we get

$d=1\\\\a=p+q-1$

Now

$a_n=p+q-1+(n-1)\times(-1)$

The $r_th$ term is given by

$a_r=p+q-1+(r-1)\times(-1)$

$a_r=p+q-r$

Hence the rth term is calculated