The 9th term is 2304
Explanation:
Given:
geometric sequence 9,−18,36,...
To find:
The 9th term
The formula for nth term of a geometric sequence is given as:
[tex]\begin{gathered} a_n\text{ = ar}^{n-1} \\ where\text{ r = common ratio} \\ n\text{ = number of terms} \end{gathered}[/tex]First we need to find r common ratio:
common rato = next term/previous term
comon ratio = -18/9 = 36/-18
common ratio = -2
[tex]\begin{gathered} when\text{ n = 9} \\ a\text{ = 9} \\ a_9\text{ = 9 }\times-2^{9-1} \\ a_9\text{ = 9 }\times-2^8 \\ \\ a_9\text{ = 2304} \end{gathered}[/tex]The 9th term is 2304
