Hello there!
Given the sequence:
[tex] \displaystyle \large{ 1, - 3,9, - 27,...}[/tex]
The question reveals it to be geometric sequence since it has common ratio.
Geometric Sequence / Ratio Formula
[tex] \displaystyle \large{r = \frac{a_{n + 1}}{a_n} }[/tex]
Define 'r' as common ratio.
First, let's check the common ratio by using the formula above.
Ratio Check
[tex] \displaystyle \large{r = \frac{ - 3}{1} \longrightarrow - 3 } \\ \displaystyle \large{r = \frac{ 9}{ - 3} \longrightarrow - 3 } \\ \displaystyle \large{r = \frac{ - 27}{9} \longrightarrow - 3 }[/tex]
Therefore, the common ratio or r-value is -3.
To find the 7th term of sequence, you can by using the General Geometric Terms.
General Term of Geometric
[tex] \displaystyle \large{a_n = a_1 {r}^{n - 1} }[/tex]
a1 is defined as the first term of sequence.
r is common ratio.
n is the term.
Since we want to find 7th term:
[tex] \displaystyle \large{a_7 =1{( - 3)}^{7 - 1} } \\ \displaystyle \large{a_7 =1{( - 3)}^{6} } \\ \displaystyle \large{a_7 =729 }[/tex]
Therefore, the 7th term of this sequence is 729.
Let me know if you have any questions!
Topic: Sequence and Series / Geometric Sequence
