[tex]\text{ nth term of a geometric sequence,}~ a_n = ar^{n-1}\\\\\text{Given that,}\\\\a_1 = ar^0 = a =0.5~~~...(i)\\\\a_5 = ar^4 = 312.5~~~~~~...(ii)\\\\\\(ii) \div (i):\\\\\\~~~~~\dfrac{ar^4}{a} = \dfrac{312.5}{0.5}=625\\\\\implies r^4 = 625\\\\\implies r=5\\\\\\\text{Now,}\\\\\\a_2 = ar=0.5 \times 5 = 2.5\\\\a_3 = ar^2 = 0.5 \times 5^2 = 12.5\\\\a_4 = ar^3 = 0.5 \times 5^3 = 62.5[/tex]
