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Previous Year Question (PYQs)



In an A.P. the $p^{th}$ term is $q$ and the $(p+q)^{th}$ term is $0$. Then the $q^{th}$ term is:






Solution

Let first term = $a$, common difference = $d$. Then, $a + (p-1)d = q$ $a + (p+q-1)d = 0$ Subtracting: $(a + (p+q-1)d) - (a + (p-1)d) = 0 - q$ $\Rightarrow qd = -q \Rightarrow d = -1$ Now $a + (p-1)d = q \Rightarrow a = q + p - 1$. $q^{th}$ term = $a + (q-1)d = (q + p - 1) - (q - 1) = p$. $\boxed{\text{Answer: (B) }p}$


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