15.2:

100; 105; 115; 120; 125; 130

15.3

1)

[tex]an = n + 4 \\ a1 = 1 + 4 = 5 \\ a2 = 2 + 4 = 6 \\ a3 = 3 + 4 = 7 \\ a4 = 4 + 4 = 8[/tex]

2)

[tex]an = 4n - 3 \\ a1 = 4 \times 1 - 3 = 1 \\ a2 = 4 \times 2 - 3 = 8 - 3 = 5 \\ a3 = 4 \times 3 - 3 = 12 - 3 = 9 \\ a4 = 4 \times 4 - 3 = 16 - 3 = 13[/tex]

3)

[tex]an = \frac{n}{ {n}^{2} + 1} \\ a1 = \frac{1}{ {1}^{2} + 1} = \frac{1}{2} \\ a2 = \frac{2}{ {2}^{2} + 1} = \frac{2}{4 + 1} = \frac{2}{5} \\ a3 = \frac{3}{ {3}^{2} + 1} = \frac{3}{9 + 1} = \frac{3}{10} \\ a4 = \frac{4}{ {4}^{2} + 1} = \frac{4}{16 + 1} = \frac{4}{17} [/tex]

4)

[tex]an = \frac{ {2}^{n} }{n} \\ a1 = \frac{ {2}^{1} }{1} = 2 \\ a2 = \frac{ {2}^{2} }{2} = \frac{4}{2} = 2 \\ a3 = \frac{ {2}^{3} }{3} = \frac{8}{3} = 2 \frac{2}{3} \\ a4 = \frac{ {2}^{4} }{4} = \frac{16}{4} = 4[/tex]

15.4 1)

[tex]bn = \frac{10}{n} \\ b2 = \frac{10}{2} = 5 \\ b7 = \frac{10}{7} = 1 \frac{3}{7} \\ b100 = \frac{10}{100} = 0.1[/tex]

2)

[tex]bn = 5 - 2n \\ b2 = 5 - 2 \times 2 = 5 - 4 = 1 \\ b7 = 5 - 2 \times 7 = 5 - 14 = - 9 \\ b100 = 5 - 2 \times 100 = 5- 200 = - 195[/tex]

3)

[tex]bn = {n}^{2} + 2n \\ b2 = {2}^{2} + 2 \times 2 = 4 + 4 = 8 \\ b7 = {7}^{2} + 2 \times 7 = 49 + 14 = 63 \\ b100 = {100}^{2} + 2 \times 100 = \\ = 10000 + 200 = 10200[/tex]

4)

[tex]bn = {( - 1)}^{n + 1} \\ b2 = {( - 1)}^{2 + 1} = {( - 1)}^{3} = - 1 \\ b7 = {( - 1)}^{7 + 1} = {( - 1)}^{8} = 1 \\ b100 = {( - 1)}^{100 + 1} = {( - 1)}^{101} = - 1[/tex]