Question

Progressão Aritmética

Answer 1

Explicação passo-a-passo:

=> $\sf a_3$

$\sf 2\cdot a_3=a_2+a_4$

$\sf 2\cdot a_3=1+\dfrac{7}{3}$

$\sf 2\cdot a_3=\dfrac{3+7}{3}$

$\sf 2\cdot a_3=\dfrac{10}{3}$

$\sf a_3=\dfrac{\frac{10}{3}}{2}$

$\sf a_3=\dfrac{10}{3}\cdot\dfrac{1}{2}$

$\sf a_3=\dfrac{10}{6}$

$\sf a_3=\dfrac{5}{3}$

=> Razão

$\sf r=a_4-a_3$

$\sf r=\dfrac{7}{3}-\dfrac{5}{3}$

$\sf r=\dfrac{2}{3}$

=> $\sf a_1$

$\sf a_1+r=a_2$

$\sf a_1+\dfrac{3}{3}=1$

$\sf a_1=1-\dfrac{2}{3}$

$\sf a_1=\dfrac{3-2}{3}$

$\sf a_1=\dfrac{1}{3}$

=> $\sf a_5$

$\sf a_5=a_4+r$

$\sf a_5=\dfrac{7}{3}+\dfrac{2}{3}$

$\sf a_5=\dfrac{9}{3}$

$\sf a_5=3$

Assim, a PA é:

$\sf PA\Big(\dfrac{1}{3},~1,~\dfrac{5}{3},~\dfrac{7}{3},~3\Big)$

• Opção 1 => Falsa

$\sf a_1+a_3=\dfrac{1}{3}+\dfrac{5}{3}$

$\sf a_1+a_3=\dfrac{6}{3}$

$\sf a_1+a_3=2$

• Opção 2 => Falsa

$\sf a_5-a_1=3-\dfrac{1}{3}$

$\sf a_5-a_1=\dfrac{9-1}{3}$

$\sf a_5-a_1=\dfrac{8}{3}$

• Opção 3 => Falsa

$\sf a_1+a_5=\dfrac{1}{3}+3$

$\sf a_1+a_5=\dfrac{1+9}{3}$

$\sf a_1+a_5=\dfrac{10}{3}$

• Opção 4 => Falsa

$\sf a_1+a_4=\dfrac{1}{3}+\dfrac{7}{3}$

$\sf a_1+a_4=\dfrac{8}{3}$

• Opção 5 => Verdadeira

$\sf a_2+a_5=1+3$

$\sf \red{a_2+a_5=4}$

=> Resposta: opção 5