Question

Numa P.G temos a1=1/4,e a7 =16 . Calcule a razão desta P.G

Answer 1

P.G(1/4
A 7 = A 1 . q^n - 1
a 7 = 1/4 . q^7 - 1
a 7 = 1/4 . q^6
1/4. q^6 = 16
q^6 = 16 : 1/4
q^6 = 16 *4/1
q^6 = 64
q^6 = 2 ^6
q = 2
A razão é 2

Answer 2

✅ Após ter terminado os cálculos, concluímos que a razão da referida progressão geométrica é:

             $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf r = 2\:\:\:}}\end{gathered} }$

Sejam os dados:

                $\Large\begin{cases} A_{1} = 1/4\\A_{7} = 16\end{cases}$

Sabendo que a fórmula do termo geral da P.G. é:

$\Large\displaystyle\begin{gathered} \bf(I)\end{gathered}$         $\Large\displaystyle\begin{gathered} A_{n} = A_{1}\cdot q^{n - 1}\end{gathered}$

Substituindo os valores na equação "I", temos:

            $\Large\displaystyle\begin{gathered} 16 = \bigg(\frac{1}{4}\bigg)\cdot q^{7 - 1}\end{gathered}$

            $\Large\displaystyle\begin{gathered} 16 = \bigg(\frac{1}{4}\bigg)\cdot q^6\end{gathered}$

           $\Large\displaystyle\text{ \begin{gathered} \frac{16}{\frac{1}{4}} = q^{6}\end{gathered} }$

     $\Large\displaystyle\begin{gathered} 16\cdot 4 = q^{6}\end{gathered}$

           $\Large\displaystyle\begin{gathered} 64 = q^{6}\end{gathered}$

             $\Large\displaystyle\begin{gathered} q = \sqrt[6]{64}\end{gathered}$

              $\Large\displaystyle\begin{gathered} q = 2\end{gathered}$

✅ Portanto, a razão procurada é:

                 $\Large\displaystyle\begin{gathered} r = 2\end{gathered}$

Saiba mais:

1. https://brainly.com.br/tarefa/6391313
2. https://brainly.com.br/tarefa/15870726
3. https://brainly.com.br/tarefa/2424374
4. https://brainly.com.br/tarefa/20223818
5. https://brainly.com.br/tarefa/6216721
6. https://brainly.com.br/tarefa/12165233
7. https://brainly.com.br/tarefa/28139571
8. https://brainly.com.br/tarefa/43780585
9. https://brainly.com.br/tarefa/33434827
10. https://brainly.com.br/tarefa/38012705
11. https://brainly.com.br/tarefa/44906804
12. https://brainly.com.br/tarefa/21823604
13. https://brainly.com.br/tarefa/18789879
14. https://brainly.com.br/tarefa/18204933
15. https://brainly.com.br/tarefa/16417760
16. https://brainly.com.br/tarefa/19419807
17. https://brainly.com.br/tarefa/43563072
18. https://brainly.com.br/tarefa/20327732
19. https://brainly.com.br/tarefa/7088479
20. https://brainly.com.br/tarefa/20420
21. https://brainly.com.br/tarefa/676115
22. https://brainly.com.br/tarefa/675941
23. https://brainly.com.br/tarefa/42181366
24. https://brainly.com.br/tarefa/39897239
25. https://brainly.com.br/tarefa/1731332
26. https://brainly.com.br/tarefa/12445301
27. https://brainly.com.br/tarefa/11064944
28. https://brainly.com.br/tarefa/5765156
29. https://brainly.com.br/tarefa/10922079