how to write code for argmin {1/2*norm(​t-xn)^2+1/​8n*(5-xn)*​xn*(t-xn)} where tbelongs to [0,2] and x1=1 and n=1,2,3,...

as, argmnargmin {1/2*norm(t-x1)^2+1/8n*(5-x1)*x1*(t-x1)} where tbelongs to [0,2] and x1=1 and n=1,2,3,...}

i want this loop to be continue n=1,2,3......