Progression: ( \left( \dfrac{3}{7} \right)^{10},\ \left( \dfrac{10}{7} \right)^{10},\ \left( \dfrac{17}{7} \right)^{10},\ \ldots )
The bases form an A.P.: ( 3, 10, 17, \ldots ) with common difference 7.
General term of the bases: ( 3 + (n-1)\cdot 7 = 7n - 4 )
Thus the ( n^{th} ) term of the given progression is [ a_n = \left( \dfrac{7n - 4}{7} \right)^{10} ]
Is it an A.P.?
No, because the terms are raised to the 10th power; the difference between consecutive terms is not constant.
Answer: ( a_n = \left( \dfrac{7n-4}{7} \right)^{10} ); No