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Question: If the \(p ^ { t h }\) term of an A.P. be \(q\) and <img src="https://cdn.pureessence.tech/canvas_...

If the pthp ^ { t h } term of an A.P. be qq and term be p, then its rthr ^ { t h } term will be.

A

p+q+rp + q + r

B

p+q−rp + q - r

C

p+r−qp + r - q

D

p−q−rp - q - r

Answer

p+q−rp + q - r

Explanation

Solution

Given that, Tp=a+(p−1)d=qT _ { p } = a + ( p - 1 ) d = q …..(i)

and Tq=a+(q−1)d=pT _ { q } = a + ( q - 1 ) d = p ….. (ii)

From (i) and (ii), we get d=−(p−q)(p−q)=−1d = - \frac { ( p - q ) } { ( p - q ) } = - 1

Putting value of in equation (i), then a=p+q−1a = p + q - 1

Now, term is given by A.P.

Tr=a+(r−1)d=(p+q−1)+(r−1)(−1)T _ { r } = a + ( r - 1 ) d = ( p + q - 1 ) + ( r - 1 ) ( - 1 ) =p+q−r= p + q - r

Note : Students should remember this question as a

formula.