Question

Find the 9th term of the geometric sequence 9,−18,36,...

Answer 1

Answer:

The 9th term is 2304

Step-by-step explanation:

Given:

geometric sequence 9,−18,36,...

To find:

The 9th term

The formula for nth term of a geometric sequence is given as:

`\begin{gathered} a_n\text{ = ar}^(n-1) \\ where\text{ r = common ratio} \\ n\text{ = number of terms} \end{gathered}`

First we need to find r common ratio:

common rato = next term/previous term

comon ratio = -18/9 = 36/-18

common ratio = -2

`\begin{gathered} when\text{ n = 9} \\ a\text{ = 9} \\ a_9\text{ = 9 }*-2^(9-1) \\ a_9\text{ = 9 }*-2^8 \\ \\ a_9\text{ = 2304} \end{gathered}`

The 9th term is 2304