[tex]a = 10000 [/tex]
[tex]r = 0.4 = 4/10 = 2/5[/tex]
[tex]a_9 = ar^8 = 10000 × 2^8/5^8[/tex]
[tex]a_9 = 10000 × 256/(25 × 25 × 25 × 25)[/tex]
[tex]a_9 = 6.5536 [/tex]
The 9th term of the given geometric sequence is 6.5536.
A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r.
[tex]a_{n} = ar^{n-1}[/tex]
Where,
[tex]a_{n}[/tex] is the nth term of geometric sequence
r is the common ratio
a is the first term of geometric sequence
According to the given question we have
First term of geometric sequence, a = 10,000
common ratio, r = 0.4
Therefore, the 9th term of the sequence is given by
[tex]a_{9} = 10000(0.4)^{9-1}[/tex]
⇒[tex]a_{9} = 10000(0.4)^{8}[/tex]
⇒ [tex]a_{9}= 10000(0.00065536)[/tex]
⇒ [tex]a_{9} = 6.5536[/tex]
Hence, the 9th term of the given geometric sequence is 6.5536.
Learn more about the geometric sequence here:
https://brainly.com/question/11266123
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