menentukan suku barisan dan deret aritmatika
Answer (1)
Penyelesaian1. a. [tex]U_n = 3n - 1[/tex][tex]U_1 = 3(1) - 1 = 2[/tex][tex]U_2 = 3(2) - 1 = 5[/tex][tex]U_3 = 3(3) - 1 = 8[/tex][tex]U_4 = 3(4) - 1 = 11[/tex][tex]U_5 = 3(5) - 1 = 14[/tex]b. [tex]U_n = \frac{1}{2}n^2 + 2n + 5[/tex][tex]U_1 = \frac12(1)^2 + 2(1) + 5 = \frac12 + 2 + 5[/tex][tex]= 7.5[/tex][tex]U_2 = \frac12(4) + 2(2) + 5 = 2 + 4 + 5[/tex][tex]= 11[/tex][tex]U_3 = \frac12(9) + 2(3) + 5 = 4.5 + 6 + 5[/tex][tex]= 15.5[/tex][tex]U_4 = \frac12(16) + 2(4) + 5 = 8 + 8 + 5[/tex][tex]= 21[/tex][tex]U_5 = \frac12(25) + 2(5) + 5 = 12.5 + 10 + 5[/tex][tex]= 27.5[/tex]c. [tex]U_n = \frac{n^2 - 4n}{2 + 3n}[/tex][tex]U_1 = \frac{1 - 4}{2 + 3} = \frac{-3}{5} = -\frac{3}{5}[/tex][tex]U_2 = \frac{4 - 8}{2 + 6} = \frac{-4}{8} = -\frac12[/tex][tex]U_3 = \frac{9 - 12}{2 + 9} = \frac{-3}{11}[/tex][tex]U_4 = \frac{16 - 16}{2 + 12} = \frac{0}{14} = 0[/tex][tex]U_5 = \frac{25 - 20}{2 + 15} = \frac{5}{17}[/tex]2. [tex]a. U_n = n^2 - 2n[/tex][tex]U_1 = 1 - 2 = -1[/tex][tex]U_2 = 4 - 4 = 0[/tex][tex]U_3 = 9 - 6 = 3[/tex][tex]U_4 = 16 - 8 = 8[/tex][tex]U_5 = 25 - 10 = 15[/tex][tex]U_6 = 36 - 12 = 24[/tex][tex]U_7 = 49 - 14 = 35[/tex]b. [tex]U_n = \frac{1}{n+3}[/tex][tex]U_1 = \frac{1}{4}[/tex][tex]U_2 = \frac{1}{5}[/tex][tex]U_3 = \frac{1}{6}[/tex][tex]U_4 = \frac{1}{7}[/tex][tex]U_5 = \frac{1}{8}[/tex][tex]U_6 = \frac{1}{9}[/tex][tex]U_7 = \frac{1}{10}[/tex]c. [tex]U_n = \frac{n}{n^2 + 1}[/tex][tex]U_1 = \frac{1}{2}[/tex][tex]U_2 = \frac{2}{5}[/tex][tex]U_3 = \frac{3}{10}[/tex][tex]U_4 = \frac{4}{17}[/tex][tex]U_5 = \frac{5}{26}[/tex][tex]U_6 = \frac{6}{37}[/tex][tex]U_7 = \frac{7}{50}[/tex]d. [tex]U_n = \frac{(-1)^n}{n+1}[/tex][tex]U_1 = \frac{-1}{2}[/tex][tex]U_2 = \frac{1}{3}[/tex][tex]U_3 = \frac{-1}{4}[/tex][tex]U_4 = \frac{1}{5}[/tex][tex]U_5 = \frac{-1}{6}[/tex][tex]U_6 = \frac{1}{7}[/tex][tex]U_7 = \frac{-1}{8}[/tex]e. [tex]U_n = n^3 - 2n^2 + 5[/tex][tex]U_1 = 1 - 2 + 5 = 4[/tex][tex]U_2 = 8 - 8 + 5 = 5[/tex][tex]U_3 = 27 - 18 + 5 = 14[/tex][tex]U_4 = 64 - 32 + 5 = 37[/tex][tex]U_5 = 125 - 50 + 5 = 80[/tex][tex]U_6 = 216 - 72 + 5 = 149[/tex][tex]U_7 = 343 - 98 + 5 = 250[/tex]
