Question

determine os sete primeiros termos de cada sequência nos seguinges caso, sendo n E N
an=10+ n
an=4n- 1
an= 2n
an= 8-2n

Answer 1

Explicação passo-a-passo:

a) $a_n=10+n$

$a_1=10+1~\longrightarrow~a_1=11$

$a_2=10+2~\longrightarrow~a_2=12$

$a_3=10+3~\longrightarrow~a_3=13$

$a_4=10+4~\longrightarrow~a_4=14$

$a_5=10+5~\longrightarrow~a_5=15$

$a_6=10+6~\longrightarrow~a_6=16$

$a_7=10+7~\longrightarrow~a_7=17$

(11, 12, 13, 14, 15, 16, 17)

b) $a_n=4n-1$

$a_1=4\cdot1-1~\longrightarrow~a_1=4-1~\longrightarrow~a_1=3$

$a_2=4\cdot2-1~\longrightarrow~a_2=8-1~\longrightarrow~a_2=7$

$a_3=4\cdot3-1~\longrightarrow~a_3=12-1~\longrightarrow~a_3=11$

$a_4=4\cdot4-1~\longrightarrow~a_4=16-1~\longrightarrow~a_4=15$

$a_5=4\cdot5-1~\longrightarrow~a_5=20-1~\longrightarrow~a_5=19$

$a_6=4\cdot6-1~\longrightarrow~a_6=24-1~\longrightarrow~a_6=23$

$a_7=4\cdot7-1~\longrightarrow~a_7=28-1~\longrightarrow~a_7=27$

(3, 7, 11, 15, 19, 23, 27)

c) $a_n=2n$

$a_1=2\cdot1~\longrightarrow~a_1=2$

$a_2=2\cdot2~\longrightarrow~a_2=4$

$a_3=2\cdot3~\longrightarrow~a_3=6$

$a_4=2\cdot4~\longrightarrow~a_4=8$

$a_5=2\cdot5~\longrightarrow~a_5=10$

$a_6=2\cdot6~\longrightarrow~a_6=12$

$a_7=2\cdot7~\longrightarrow~a_7=14$

(2, 4, 6, 8, 10, 12, 14)

d) $a_n=8-2n$

$a_1=8-2\cdot1~\longrightarrow~a_1=8-2~\longrightarrow~a_1=6$

$a_2=8-2\cdot2~\longrightarrow~a_2=8-4~\longrightarrow~a_2=4$

$a_3=8-2\cdot3~\longrightarrow~a_3=8-6~\longrightarrow~a_3=2$

$a_4=8-2\cdot4~\longrightarrow~a_4=8-8~\longrightarrow~a_4=0$

$a_5=8-2\cdot5~\longrightarrow~a_5=8-10~\longrightarrow~a_5=-2$

$a_6=8-2\cdot6~\longrightarrow~a_6=8-12~\longrightarrow~a_6=-4$

$a_7=8-2\cdot7~\longrightarrow~a_7=8-14~\longrightarrow~a_7=-6$

(6, 4, 2, 0, -2, -4, -6)