Question

Considerando a lei de formação an=2n+5
Calcule :
a) a2 - a1=
b) 2a3 + a4=
c) a5. a2=
d) a3. 2a1=

Answer 1

Vamos, primeiramente, calcular a1, a2, a3, a4 e a5.

$a_1~=~2\,.\,1~+~5\\\\a_1~=~2~+~5\\\\\boxed{a_1~=~7}\\\\\\a_2~=~2\,.\,2~+~5\\\\a_2~=~4~+~5\\\\\boxed{a_2~=~9}\\\\\\a_3~=~2\,.\,3~+~5\\\\a_3~=~6~+~5\\\\\boxed{a_3~=~11}\\\\\\a_4~=~2\,.\,4~+~5\\\\a_4~=~8~+~5\\\\\boxed{a_4~=~13}\\\\\\a_5~=~2\,.\,5~+~5\\\\a_5~=~10~+~5\\\\\boxed{a_5~=~15}$

Agora, calculando as expressões:

a)

$a_2~-~a_1~=~9~-~7\\\\\boxed{a_2~-~a_1~=~2}$

b)

$2a_3~+~a_4~=~2\,.\,11~+~13\\\\2a_3~+~a_4~=~22~+~13\\\\\boxed{2a_3~+~a_4~=~35}$

c)

$a_5~.~a_2~=~15~.~9\\\\\boxed{a_5~.~a_2~=~135}$

d)

$a_3~.~2a_1~=~11~.~2\,.\,7\\\\a_3~.~2a_1~=~22~.~7\\\\\boxed{a_3~.2a_1~=~154}$