[latex]a) a_n=3n \ a_1=3*1=1 a_2=3*2=6 a_3=3*3=9 \ a_4=3*4=12 a_5=3*5=15 \ b)a_n=n^3-n^2 \ a_1=1^3-1^2=1-1=0 \ a_2=2^3-2^2=8-4=4 \ a_3=3^3-3^2=27-9=18 \ a_4=4^3-4^2=64-16=48 \ a_5=5^3-5^2=125-25=100 \ c)a_n= frac{n}{2^n} \ a_1= frac{1}{2^1} = frac{1}{2} \ a_2= frac{2}{2^2} = frac{2}{4} = frac{1}{2} \ a_3= frac{3}{2^3} = frac{3}{8} \ a_4= frac{4}{2^4} = frac{4}{16} = frac{1}{4} \ a_5= frac{5}{2^5} = frac{5}{32} \ d)a_n= frac{3}{n(n+2)} \ a_1= frac{3}{1(1+2)} =1 \ [/latex] a_2=[latex]a_2= frac{3}{2(2+2)} = frac{3}{2*4} = frac{3}{8} \ a_3= frac{3}{3(3+2} = frac{3}{3*5} = frac{1}{5} \ a_4= frac{3}{4(4+2)} = frac{3}{4*6} = frac{3}{24} = frac{1}{8} \ a_5= frac{3}{5(5+2)} = frac{3}{5*7} = frac{3}{35} [/latex]
