Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Discover a wealth of knowledge from experts across different disciplines on our comprehensive Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

Write a recursive formula for the following sequence and also identify the seventh them. You are welcome to submit an image of handwritten work. If you choose to type then use the following notation to indicate terms; a_n and a_(n-1). To earn full credit be sure to share all work/calculations and thinking.a_n = {-2, \frac{2}{3}, -\frac{2}{9}, \frac{2}{27}}

Write A Recursive Formula For The Following Sequence And Also Identify The Seventh Them You Are Welcome To Submit An Image Of Handwritten Work If You Choose To class=

Sagot :

EXPLANATION:

We are given a sequence and the first and second terms are;

[tex]\begin{gathered} a_1=-2 \\ a_2=\frac{2}{3} \end{gathered}[/tex]

The common ratio is determined by dividing a term by its preceeding term. Hence, we can derive the common ratio by dividing the second term by the first.

[tex]\begin{gathered} Common\text{ }ratio: \\ r=\frac{2}{3}\div\frac{-2}{1} \end{gathered}[/tex][tex]r=\frac{2}{3}\times\frac{1}{-2}[/tex][tex]r=-\frac{1}{3}[/tex]

The recursive formula for this sequence would be given as follows;

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

Where the variables are;

[tex]\begin{gathered} a_n=nth\text{ term} \\ r=-\frac{1}{3} \end{gathered}[/tex]

We now have;

[tex]a_n=a_{n-1}(-\frac{1}{3})[/tex]

For the 5th term we would have;

[tex]a_5=a_4(-\frac{1}{3})[/tex][tex]a_5=\frac{2}{27}(-\frac{1}{3})[/tex][tex]a_5=-\frac{2}{81}[/tex]

For the 6th term we would have;

[tex]a_6=a_5(-\frac{1}{3})[/tex][tex]a_6=-\frac{2}{81}\times(-\frac{1}{3})[/tex][tex]a_6=\frac{2}{243}[/tex]

For the 7th term we would have;

[tex]a_7=a_6(-\frac{1}{3})[/tex][tex]a_7=\frac{2}{243}(-\frac{1}{3})[/tex][tex]a_7=-\frac{2}{729}[/tex]

ANSWER:

[tex]\begin{gathered} Recursive\text{ }formula: \\ a_n=a_{n-1}(-\frac{1}{3}) \\ 7th\text{ }term: \\ a_7=-\frac{2}{729} \end{gathered}[/tex]

Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.