Question

3- Calcule os nove primeiros termos, da P.A;
a)Em que o a1 = 9 e a razão 6
b) Em que o a1 = -4 e a razão -10
c) Em que o a1 = 45 e a razão -5​

Answer 1

Resposta:

a) $\boxed{P.A ={9, 15, 21, 27, 33, 39, 45, 51, 57}}$

b) $\boxed{PA= {-4,-14,-24,-34,-44,-54,-64,-74,-84}}$

c) $\boxed{PA={45,40,35,30,25,20,15,10,5}}$

Explicação passo-a-passo:

$a) \boxed{a_{n} = a_{1} + (n − 1)\cdot\; r}\\[0.15cm]a_{1} = 9;\; r = 6;\; n = 9\\a_{n} =a_{1} + (n − 1)\cdot\; r\\\text{Substituindo \cdots }\\a_{9} = 9 + (9 − 1)\cdot6\\[0.15cm]a_{9} =9 + 8\cdot6\\[0.15cm]a_{9} = 9 + 48\\[0.15cm]a_{9} = \boxed{57}\\[0.15cm]\boxed{P.A ={9, 15, 21, 27, 33, 39, 45, 51, 57 }}$

b)

$\boxed{a_{n}=a_{1}+(n-1)\cdot\;r}\\[0,15cm]a_{1}=-4;\;r=-10;\;n=9\\a_{n}=a_{1}+(n-1)\cdot\;r\\\text{Substituindo \cdots }\\a_{9}=-4+(9-1)\cdot(-10)\\[0,15cm]a_{9}=-4+8\cdot(-10)\\[0,15cm]a_{9}=-4-80\\[0,15cm]a_{9}=\boxed{-84}\\[0,15cm]\boxed{P,A= {-4,-14,-24,-34,-44,-54,-64,-74,-84}}$

c)

$\boxed{a_{n}=a_{1}+(n-1)\cdot\;r}\\[0,15cm]a_{1}=45;\;r=-5;\;n=9\\a_{n}=a_{1}+(n-1)\cdot\;r\\\text{Substituindo \cdots }\\a_{9}=45+(9-1)\cdot(-5)\\[0,15cm]a_{9}=45+8\cdot(-5)\\[0,15cm]a_{9}=45-40\\[0,15cm]a_{9}=\boxed{5}\\[0,15cm]\boxed{P,A={45,40,35,30,25,20,15,10,5}}$

Bons estudos.