Question

1 – Escreva uma PG de 5 termos em que a1 = 5 e q = 3.

o restante da atividade está na imagem​

Answer 1

$\large\boxed{\begin{array}{l}\rm 1)~Escreva~a~PG~de~5~termos\\\rm em~que~a_1=5~e~q=3\\\underline{\bf soluc_{\!\!,}\tilde ao:}\\\sf a_2=5\cdot3=15\\\sf a_3=15\cdot3=45\\\sf a_4=45\cdot3=135\\\sf a_5=135\cdot3=405\\\sf(5,15,45,135,405)\end{array}}$

$\large\boxed{\begin{array}{l}\rm 2)~Determi e~o~d\acute ecimo~termo~da~PG\,(1,2,4...)\\\underline{\bf soluc_{\!\!,}\tilde ao:}\\\sf q=\dfrac{2}{1}=2\\\sf a_{10}=a_3\cdot q^7\\\sf a_{10}=4\cdot2^7\\\sf a_{10}=4\cdot128\\\sf a_{10}=512\end{array}}$

$\large\boxed{\begin{array}{l}\rm 3)~Determine~o~oitavo~termo~da~PG\,(1,3,9,...)\\\underline{\bf soluc_{\!\!,}\tilde ao:}\\\sf q=\dfrac {3}{1}=3\\\sf a_8=a_3\cdot q^5\\\sf a_8=9\cdot 3^5\\\sf a_8=9\cdot243\\\sf a_8=2187\end{array}}$

$\large\boxed{\begin{array}{l}\rm 4)~Qual~o~sexto~termo~da~PG\,(512,256,...)\\\underline{\bf soluc_{\!\!,}\tilde ao:}\\\sf q=\dfrac{256}{512}=\dfrac{1}{2}\\\sf a_6=a_2\cdot q^4\\\sf a_6=256\cdot\bigg(\dfrac{1}{2}\bigg)^4\\\sf a_6=256\cdot\dfrac{1}{16}\\\sf a_6=\dfrac{256}{16}\\\sf a_6=16\end{array}}$