Answered

Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Join our Q&A platform and get accurate answers to all your questions from professionals across multiple disciplines. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Find the indicated term of the geometric series using the recursive formula.
1, 6, 36, 216, ...

Sagot :

jacob193

Answer:

[tex]1296[/tex] would be the term immediately after the term [tex]216[/tex].

Step-by-step explanation:

The recursive formula for the [tex]n[/tex]th term a geometric series is:

[tex]a_{n} = r\, a_{n - 1}[/tex],

Where:

  • [tex]r[/tex] is the common ratio of this series, and
  • [tex]a_{n - 1}[/tex] denotes the [tex](n-1)[/tex]th term of the series, which is the term immediately before the [tex]n[/tex]th term.

The common ratio of a geometric series is the ratio between each term and the term before it- for example, the ratio between the term [tex]36[/tex] and the term right before it, [tex]6[/tex]. Using this property, the common ratio of the geometric series in this question would be:

[tex]\displaystyle r = \frac{36}{6} = 6[/tex].

In this question, if [tex]a_{n}[/tex] represents the unknown term,  [tex]216[/tex] would be the value of [tex]a_{n-1}[/tex], which is immediately before that unknown term. Since the common ratio is [tex]r = 6[/tex], the value of the unknown term [tex]a_{n}[/tex] can be found using the recursive formula as follows:

[tex]a_{n} = r\, a_{n - 1} = (6) \times (216) = 1296[/tex].

Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.