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Given a1 = 1/4 and a common ratio of 8,find the 9th term in the sequence.​

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billjo95

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a1=-256

r= -1/4

Approximated the sum of the first 17 terms to the nearest tenth. Sum= -204.8

The 9th term in the geometric sequence is 4194304.

What is geometric Sequence?

"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.

Learn more about geometric sequence here

https://brainly.com/question/11266123

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