If {p^{th}} term of an A.P. be q and {q^{th}} term be p , then its {r^{th}} term will be

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8. Sequences and Series

easy

If the ${p^{th}}$ term of an $A.P.$ 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

$p - q - r$

Solution

(b) Given that, ${T_p} = a + (p – 1)d = q$ …..$(i)$

and ${T_q} = a + (q – 1)d = p$ ….. $(ii)$

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

Putting value of $d$ in equation $(i),$ then $a = p + q – 1$

Now, ${r^{th}}$ term is given by $A.P.$

${T_r} = a + (r – 1)d = (p + q – 1) + (r – 1)( – 1)$ $ = p + q – r$

Note : Students should remember this question as a formula.

Standard 11

Mathematics

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