Question

Escreva os quatro primeiros termos das sequências dadas (comece pelo n = 1).


a) an = 3n – 1

b) an = n – 1

c) an = 5n

​

Answer 1

Basta substituirmos "n" pela posição do termo desejado.

a)

$\underline{1^o\,Termo~\rightarrow~n=1}:\\\\a_1~=~3\cdot1~-~1\\\\a_1~=~3~-~1\\\\\boxed{a_1~=~2}\\\\\\\underline{2^o\,Termo~\rightarrow~n=2}:\\\\a_2~=~3\cdot2~-~1\\\\a_2~=~6~-~1\\\\\boxed{a_2~=~5}\\\\\\\underline{3^o\,Termo~\rightarrow~n=3}:\\\\a_3~=~3\cdot3~-~1\\\\a_3~=~9~-~1\\\\\boxed{a_3~=~8}\\\\\\\underline{4^o\,Termo~\rightarrow~n=4}:\\\\a_4~=~3\cdot4~-~1\\\\a_4~=~12~-~1\\\\\boxed{a_4~=~11}$

A sequencia fica:  {2 , 5 , 8 , 11}

b)

$\underline{1^o\,Termo~\rightarrow~n=1}:\\\\a_1~=~1~-~1\\\\\boxed{a_1~=~0}\\\\\\\underline{2^o\,Termo~\rightarrow~n=2}:\\\\a_2~=~2~-~1\\\\\boxed{a_2~=~1}\\\\\\\underline{3^o\,Termo~\rightarrow~n=3}:\\\\a_3~=~3~-~1\\\\\boxed{a_3~=~2}\\\\\\\underline{4^o\,Termo~\rightarrow~n=4}:\\\\a_4~=~4~-~1\\\\\boxed{a_4~=~3}$

A sequencia fica:  {0 , 1 , 2 , 3}

c)

$\underline{1^o\,Termo~\rightarrow~n=1}:\\\\a_1~=~5\cdot1\\\\\boxed{a_1~=~5}\\\\\\\underline{2^o\,Termo~\rightarrow~n=2}:\\\\a_2~=~5\cdot2\\\\\boxed{a_2~=~10}\\\\\\\underline{3^o\,Termo~\rightarrow~n=3}:\\\\a_3~=~5\cdot3\\\\\boxed{a_3~=~15}\\\\\\\underline{4^o\,Termo~\rightarrow~n=4}:\\\\a_4~=~5\cdot4\\\\\boxed{a_4~=~20}$

A sequencia fica:  {5 , 10 , 15 , 20}