Question

Please help i need to get this done asap

Answer 1

`\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) / (i):\\\\\\~~~~~(ar^4)/(a) = (312.5)/(0.5)=625\\\\\implies r^4 = 625\\\\\implies r=5\\\\\\\text{Now,}\\\\\\a_2 = ar=0.5 * 5 = 2.5\\\\a_3 = ar^2 = 0.5 * 5^2 = 12.5\\\\a_4 = ar^3 = 0.5 * 5^3 = 62.5`