ANSWER
[tex]a_{23} = 219667417263[/tex]
The pattern is geometric.
EXPLANATION
The given pattern is:
7, -21, 63, -189,..
We can see from the pattern that,
[tex] r = \frac{ - 189}{63} = \frac{63}{ - 21} = \frac{ - 21}{7} = - 3[/tex]
Since there is a common ratio of -3, the pattern is geometric.
The first term of this pattern is
[tex]a_1=7[/tex]
The nth term of the pattern is given by the formula:
[tex]a_n = a_1 {r}^{n - 1} [/tex]
To find the 23rd term, we put, n=23, the first term and the constant ratio.
[tex]a_{23}= 7{ (-3 )}^{23 - 1} [/tex]
[tex]a_{23}= 7{ (-3 )}^{22} [/tex]
[tex] a_{23} = 219667417263[/tex]
