Join IDNLearn.com and start exploring the answers to your most pressing questions. Get the information you need from our community of experts who provide accurate and comprehensive answers to all your questions.
Sagot :
ANSWER:
[tex]a_n=3\cdot(-4)^{n-1}[/tex]STEP-BY-STEP EXPLANATION:
We have the following formula for nth terms
[tex]a_n=a_1\cdot r^{n-1}^{}[/tex]we replace for each point and we are left
[tex]\begin{gathered} a_2=-12 \\ -12=a_1\cdot r^{2-1}\rightarrow-12=a_1\cdot r^{}\text{ (1)} \\ a_5=768 \\ 768=a_1\cdot r^{5-1}\rightarrow768=a_1\cdot r^4\text{ (2)} \end{gathered}[/tex]We solve the system of equations that remains like this:
[tex]\begin{gathered} a_1=\frac{-12}{r}\text{ (3)} \\ a_1=\frac{768}{r^3}\text{ (4)} \\ \text{we equalize (3) and (4)} \\ -\frac{12}{r}=\frac{768}{r^4} \\ r^3=\frac{768}{-12} \\ r=\sqrt[3]{-64} \\ r=-4 \end{gathered}[/tex]Now, for a1
[tex]\begin{gathered} a_1=\frac{-12}{-4} \\ a_1=3 \end{gathered}[/tex]
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Your questions deserve reliable answers. Thanks for visiting IDNLearn.com, and see you again soon for more helpful information.
