The 9th term in the geometric sequence is 4194304.
"A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence. In other words, in a geometric sequence, every term is multiplied by a constant which results in its next term. So a geometric sequence is in form a, ar, a[tex]r^{2}[/tex]... where 'a' is the first term and 'r' is the common ratio of the sequence. The common ratio can be either a positive or a negative real number."
We have
[tex]a_{1}[/tex] = [tex]\frac{1}{4}[/tex]
Common ratio (r) = 8
Formula to find 9th term in the geometric sequence
[tex]a_{n}= a_{1} r^{n-1}[/tex]
⇒[tex]a_{9}= \frac{1}{4}[/tex] × [tex]8^{(8-1)}[/tex]
⇒[tex]a_{9}= \frac{1}{4}[/tex] × [tex]8^{8}[/tex]
⇒[tex]a_{9}= \frac{1}{4}[/tex] × [tex]16777216[/tex]
⇒[tex]a_{9} =4194304[/tex]
Hence, the 9th term in the geometric sequence is 4194304.
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