israelgonzalez1212
Answered

Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

What is the explicit formula for the geometric sequence with this recursive
formula?
a =
8
2.-1
(
O A... ----(3)
O B.
11
1
6
• (-4)(n-1)
OC. ,- 1.(-6)(n-1)
=
OD. 2, --5•()
160

What Is The Explicit Formula For The Geometric Sequence With This Recursive Formula A 8 21 O A 3 O B 11 1 6 4n1 OC 16n1 OD 2 5 160 class=

Sagot :

AliceBrainly21

Answer:

D)

[tex]an = -6 \times {( \frac{1}{4} )}^{n - 1} [/tex]

Step-by-step explanation:

(See the picture)

View image AliceBrainly21
abidemiokin

The explicit formula is given as [tex]T_n=-6(\frac{1}{4} )^{n-1}[/tex]

Geometric and recursive functions

The general explicit formula for a geometric sequence is expressed as:

  • [tex]T_n=ar^{n-1}[/tex]

Given the following recursive functions:

[tex]a_1=-6\\ a_n=a_{n-1}\cdot\frac{1}{4} [/tex]

Get the next two terms:

[tex]a_2=a_{1}\cdot\frac{1}{4} \\ a_2=-6\cdot\frac{1}{4} \\ a_2=\frac{-3}{2} [/tex]

For the third term:

[tex]a_3=a_{2}\cdot\frac{1}{4} \\ a_3=\frac{-3}{2} \cdot\frac{1}{4} \\ a_3=\frac{-3}{8} [/tex]

The common ratio for the sequence will be [tex]\frac{1}{4} [/tex]

The explicit formula is given as [tex]T_n=-6(\frac{1}{4} )^{n-1}[/tex]

Learn more on explicit functions here: https://brainly.com/question/10308651

Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.