Q. If the $p$th term of an AP be $q\ and\ q$th term be $p$, then its $r$th term will be
A) $p + q + r$
B) $p + q - r$
C) $p + r - q$
D) $p - q - r$
Explanation
(b)
Given that $T_{p} = a + (p - 1)d = q$ …(i)
And $T_{q} = a + (q - 1)d = p$ …(ii)
From Eqs. (i) and (ii), we get
$d = - \frac{(p - q)}{p - q)} = - 1$ …(iii)
On putting the value of $d$ in Eq.(i),we get
$a + (p - 1)( - 1) = q$
$\Rightarrow a = p + q - 1$ …(iv)
Now, $r$th term is given by AP
$T_{r} = a + (r - 1)d = (p + q - 1) + (r - 1)( - 1)$
[from Eqs. (iii) and (iv)]
$= \ p + q - r$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.