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If $p^{th}, q^{th} and r^{th}$ terms of both an A.P. and a G.P. be respectively $a, b and c$ , then $a^{b} . b^{c} . c^{a} - a^{c} . b^{a} . c^{b} =$

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Detailed Solution

a = x + (p - 1) d = x . m^{p - 1}

b = x + (q - 1) d = x . m^{q - 1}

c = x + (r - 1) d = x . m^{r - 1}

$a^{b} . b^{c} . c^{a} = {(x m^{p - 1})}^{(x + (q - 1) d)} . {(x m^{q - 1})}^{(x + (r - 1) d)} . {(x m^{r - 1})}^{(x + (p - 1) d)}$

$a^{c} . b^{a} . c^{b}$ both same

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