Question

Na sequência (31, 27, 23, 19, 15, ...) os termos a2, a6, a8 são, respectivamente: *

a)27, 7, — 1

b)27, 11, 7

c)27, 11, 3

d)27, 15, 7

e)27, 10, 3

Me ajudem por favor.​

Answer 1

Resposta:

B) 27, 11, 3

Explicação passo-a-passo:

primeiro temos que descobrir o valor da razão dessa Progressão.

r = a2 - a1

r = 27 - 31

r = - 4

agora que já sabemos o valor da razão podemos usar a fórmula do termo geral para encontrar a6 e a8.

a6 :

$an = a1 + (n - 1).r \</strong><strong>\</strong><strong>a</strong><strong>_</strong><strong>{</strong><strong>6 </strong><strong>}</strong><strong>= 31 + (6 - 1). - 4 \\ a</strong><strong>_</strong><strong>{</strong><strong>6 </strong><strong>}</strong><strong>= 31 + 5. - 4 \\ a</strong><strong>_</strong><strong>{</strong><strong>6</strong><strong>}</strong><strong> = 31 +( - 20) \\ a</strong><strong>_</strong><strong>{</strong><strong>6</strong><strong>}</strong><strong> = 31 - 20</strong><strong> \\ \red{</strong><strong>\</strong><strong>b</strong><strong>o</strong><strong>x</strong><strong>e</strong><strong>d</strong><strong>{</strong><strong>a</strong><strong>_</strong><strong>{</strong><strong>6 </strong><strong>}</strong><strong>= 11</strong><strong>}</strong><strong>}</strong><strong>$

a8 :

$an = a1 + (n - 1).r \\ a</strong><strong>_</strong><strong>{</strong><strong>8</strong><strong>}</strong><strong> = 31 + (8 - 1). - 4 \\ a</strong><strong>_</strong><strong>{</strong><strong>8 </strong><strong>}</strong><strong>= 31 + 7. - 4 \\ a</strong><strong>_</strong><strong>{</strong><strong>8 </strong><strong>}</strong><strong>= 31 + ( - 28) \\ a</strong><strong>_</strong><strong>{</strong><strong>8</strong><strong>}</strong><strong> = 31 - 28 \\ \red{</strong><strong>\</strong><strong>b</strong><strong>o</strong><strong>x</strong><strong>e</strong><strong>d</strong><strong>{</strong><strong>a</strong><strong>_</strong><strong>{</strong><strong>8</strong><strong>}</strong><strong> = 3}</strong><strong>}</strong><strong>$

espero ter ajudado :)