We have: #a_(n) = frac(10)(n^(frac(2)(3)))#
To evaluate the first five terms, simply replace #n# with the number of the term:
#Rightarrow a_(1) = frac(10)(1^(frac(2)(3))) = frac(10)(1) = 10#
#Rightarrow a_(2) = frac(10)(2^(frac(2)(3))) = frac(10)((2^(2))^(frac(1)(3))) = frac(10)(root(3)(4))#
#Rightarrow a_(3) = frac(10)(3^(frac(2)(3))) = frac(10)((3^(2))^(frac(1)(3))) = frac(10)(root(3)(9))#
#Rightarrow a_(4) = frac(10)(4^(frac(2)(3))) = frac(10)((4^(2))^(frac(1)(3))) = frac(10)(root(3)(16))#
#Rightarrow a_(5) = frac(10)(5^(frac(2)(3))) = frac(10)((5^(2))^(frac(1)(3))) = frac(10)(root(3)(25))#
Therefore, the first five terms of the sequence are #10, frac(10)(root(3)(4)), frac(10)(root(3)(9)), frac(10)(root(3)(16))# and #frac(10)(root(3)(25))#
