Question

If in an A.P. pth term is q and the (p+q)th term is 0. Then, its qth term is

• A. -p
• B. p
• C. p-q
• D. p+q

Answer 1

The correct option is B p

Let the first term and common difference of the given A.P. be a and d, respectively.
$a_p=q\Rightarrow a+(p-1)d=q\Rightarrow a=q-(p-1)d{a}_{p+q}=0\Rightarrow a+(p+q-1)d=0\Rightarrow q-(p-1)d+(p+q-1)d=0\Rightarrow q-pd+d+pd+qd-d=0\Rightarrow q+qd=0\Rightarrow d=-1\therefore a=q+p-1a_q=a+(q-1)d\Rightarrow a_q=q+p-1+(q-1)(-1)\Rightarrow a_q=q+p-1-q+1\Rightarrow a_q=p$