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If $\mathrm{p}^{\text {th }}$ term of an $\mathrm{AP}$ is $\mathrm{q}$, and its $\mathrm{q}^{\text {th }}$ term is $\mathrm{p}$, then what is the common difference?
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$-1$
Let first term and common difference of an AP are a and d respectively. Its $\mathrm{P}^{\text {th }}$ term $=\mathrm{a}+(\mathrm{p}-1) \mathrm{d}=\mathrm{q}$ ...(i)
and $q^{\text {th }}$ term $=a+(q-1) d=p$ ...(ii)
Solving Eqs. (i) and (ii), we find
$a=p+q-1, d=-1$
and $q^{\text {th }}$ term $=a+(q-1) d=p$ ...(ii)
Solving Eqs. (i) and (ii), we find
$a=p+q-1, d=-1$
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