✏️SEQUENCE
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Problem: Find the 9th term of the geometric sequence: 3, 9, 27, 81,
Solution: Determine the common ratio.
[tex]\begin{aligned}&\bold{\color{lightblue}Formula:}\\& \boxed{r = \frac{a_n}{a_{n-1} } } \end{aligned}[/tex]
- [tex]\begin{aligned} r = \frac{a_2}{a_{1} } = \frac{9}{3} = 3\end{aligned}[/tex]
- [tex]\begin{aligned} r = \frac{a_3}{a_{2} } = \frac{27}{9} = 3\end{aligned}[/tex]
- [tex]\begin{aligned} r = \frac{a_4}{a_{3} } = \frac{81}{27} = 3\end{aligned}[/tex]
- Use the Geometric Sequence Formula to find the 9th term.
[tex]\begin{aligned}&\bold{\color{lightblue}Formula:}\\& \boxed{a_n= a_1 \cdot r^{n - 1} } \end{aligned}[/tex]
- [tex]{a_9= 3 \cdot 3^{9 - 1} } [/tex]
- [tex]{a_9= 3 \cdot 3^{8} } [/tex]
- [tex]{a_9= 3 \cdot 6561 } [/tex]
- [tex]{a_9= 19683 } [/tex]
- Therefore, the 9th term of the geometric sequence is:
- [tex] \large \boxed{ \sf{ \green{ \: 19683 \: }}}[/tex]
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