Question

If in an A.P., the pth term is q and (p + q)th term is zero, then the qth term is

• A. - p
• B. p
• C. p + q
• D. p - q

Answer 1

The correct option is B

p

As, $a_p=q$

$\Rightarrow a+(p-1)d=q\dots \dots \left(i\right)$

Also, $a_{(p+q)}=0$

$\Rightarrow a+(p+q-1)d=0\dots \dots \left(ii\right)$

Subtracting (i) from (ii), we get

a + (p + q - 1)d - a - (p - 1)d = 0 - q

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

$\Rightarrow qd=-q$

$\Rightarrow d=\frac{-q}{q}$

$\Rightarrow d=-1$

Substituting d = - 1 in (i) we get

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

$\Rightarrow a-p+1=q$

$\Rightarrow a=p+q-1$

Now,

$\Rightarrow a_q=a+(q-1)d$

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

$=p+q-1-q+1$

$=p$

Hence, the correct alternative is option (b).