Respuesta :
Answer:
1. 1
3. 729/8
Explanation:
Part 1
In the sequence: 729, -243, 81,...
[tex]\begin{gathered} \frac{81}{-243}=-\frac{1}{3} \\ -\frac{243}{729}=-\frac{1}{3} \end{gathered}[/tex]• The first term, a = 729
,• The common ratio, r = -1/3
The nth term of a geometric progression is obtained by the formula below:
[tex]a_n=a_1r^{n-1}[/tex]Therefore, the rule for the nth term will be:
[tex]a_n=729(-\frac{1}{3})^{n-1}[/tex]We then find a7, the seventh term.
[tex]\begin{gathered} a_7=729(-\frac{1}{3})^{7-1} \\ =729(-\frac{1}{3})^6 \\ =729\times\frac{1}{729} \\ =1 \end{gathered}[/tex]The seventh term is 1.
Part 3
In the sequence: 8, 12, 18,...
[tex]\begin{gathered} \frac{12}{8}=1.5 \\ \frac{18}{12}=1.5 \end{gathered}[/tex]• The first term, a = 8
,• The common ratio, r = 1.5
The nth term of a geometric progression is obtained by the formula below:
[tex]a_n=a_1r^{n-1}[/tex]Therefore, the rule for the nth term will be:
[tex]a_n=8(1.5)^{n-1}[/tex]We then find a7, the seventh term.
[tex]\begin{gathered} a_7=8(1.5)^{7-1} \\ =8(1.5)^6 \\ =\frac{729}{8} \\ =91\frac{1}{8} \end{gathered}[/tex]The seventh term is 729/8.
